The talks are listed in reverse chronological order, so please scroll down to find today’s talks!
We announce talks from the following set theory related seminars and colloquia:
– European Set Theory Society Colloquia, 17:00-19:00 CEST/CET, several times each year
– Kobe Set Theory Seminar, Monday 16:30 local time (09:30 CEST until 29 October 2023, 08:30 CET from 30 October 2023)
– National University of Singapore Logic Seminar, Tuesdays 17:00-18:00 local time (11:00-12:00 CEST until 29 October, then 10:00-11:00 CET)
– Baltic Set Theory Seminar, Tuesdays 15:00-16:30 local time (15:00-16:00 CEST/CET)
– Carnegie-Mellon University Pittsburgh Core Model Seminar, Tuesdays 1:30pm local time (19:30 CEST/CET, except in the week beginning with 30 October, then 18:30 CET)
– Carnegie-Mellon University Pittsburgh Logic Seminar, Tuesdays 3:30pm local time (21:30 CEST/CET, except in the week beginning with 30 October, then 20:30 CET)
– Hebrew University Set Theory Seminar, Wednesdays 13:00-15:00 local time (12:00-14:00 CET)
– Leeds Models and Sets Seminar, Wednesdays 14:00-15:00 local time (15:00-16:00 CEST/CET)
– Barcelona Set Theory Seminar, Wednesdays 4pm local time (15:00-16:30 CEST/CET)
– Caltech: Logic seminar, Wednesdays 12am-1pm local time (21:00-22:00 CEST/CET except in the week beginning with 30 October, then 20:00 CET)
– Renyi Institute Set Theory Seminar, Thursdays 10:30 – 12:00 CEST/CET
– Vienna Set Theory Seminar, Thursdays 11:30-13:00 OR Tuesdays 15:00-16:30 local time (15:00-16:00 CEST/CET)
– Vienna Logic Colloquium, Thursdays 13:30 – 14:20 local time (15:00 – 16:30 CEST/CET)
– Bristol Logic and Set Theory Seminar, Thursdays 15:00 local time (16:00 CEST/CET)
– Cross-Alps Logic Seminar, Fridays 16:00 local time (16:00 CEST/CET)
– CUNY Set Theory Seminar, Fridays 12:15pm-1:45pm local time (18:15-19:45 CEST/CET except in the week beginning with 30 October, then 17:15-18:45 CET)
– University of Toronto Set Theory seminar, Fridays 1:30pm local time (19:30 CEST/CET except in the week beginning with 30 October, then 18:30 CET)
– CUNY Logic Workshop, Fridays 2:00pm-3:30pm local time (20:00-21:30 CEST/CET except in the week beginning with 30 October, then 19:00-20:30 CET)
20 – 26 May
CMU Core Model Seminar
Time: Tuesday, 21 May, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)
Speaker:
Title:
Abstract:
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 21 May, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker:
Title:
Abstract:
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 22 May, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker:
Title:
Abstract:
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Set Theory Seminar
Time: Wednesday, 22 May, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 22 May, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker:
Title:
Abstract:
Information: See the seminar webpage.
Vienna Research Seminar in Set Theory
Time: Thursday, 23 May, 11:30-13:00 CEST
Speaker:
Title:
Abstract:
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 23 May, 15:00 – 15:50 CEST
Speaker:
Title:
Abstract:
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Cross-Alps Logic Seminar
Time: Friday, 24 May, 16.00-17.00 CEST
Speaker:
Title:
Abstract:
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
New York Set Theory Seminar
Time: Friday, 24 May, 12.30-1.45pm New York time (18.30-20.45 CEST)
Speaker:
Title:
Abstract:
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 24 May, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker:
Title:
Abstract:
Information: Please see the conference webpage for the login information.
13 – 19 May
Hebrew University Set Theory Seminar
Time: Wednesday, 15 May, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: Zhixing You
Title: The intersection of a sequence of outer models and sum ultrafilter constructions
Abstract: The technique of taking the intersection of a sequence of outer models is understudied in the field of Mathematical Logic. With Assaf Rinot and Jiachen Yuan, we find it to be quite effective for constructing some interesting sum ultrafilters. In this talk, I will use it to answer some questions about indecomposable ultrafilters and $\delta$-complete uniform ultrafilters. A sample result is that we construct a model in which there exists a weakly compact cardinal that carries an indecomposable ultrafilter but not measurable, thus answering an old question of Ketonen in the negative.
If time permits, I will isolate a criteria which can generally characterize when the ground model equals the intersection of some generic extensions and extend some results in infinitary combinatorics.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Set Theory Seminar
Time: Wednesday, 15 May, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 15 May, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker: Michael Wolman, Caltech
Title: Invariant uniformization and reducibility
Abstract: Given sets X,Y and P⊆X×Y with projX(P)=X, a uniformization of P is a function f:X→Y such that (x,f(x))∈P for all x∈X. If now E is an equivalence relation on X, we say that P is E-invariant if x1Ex2⟹Px1=Px2, where Px={y:(x,y)∈P} is the x-section of P. In this case, an E-invariant uniformization is a uniformization f such that x1Ex2⟹f(x1)=f(x2).
Consider now the situation where X,Y are Polish spaces and P is a Borel subset of X×Y. In this case, standard results in descriptive set theory provide conditions which imply the existence of Borel uniformizations. These fall mainly into two categories: “small section” and “large section” uniformization results.
Suppose now that E is a Borel equivalence relation on X, P is E-invariant, and Phas “small” or “large” sections. In this talk, we address the following question: When does there exist a Borel E-invariant uniformization of P?
We show that for a fixed E, every such P admits a Borel E-invariant uniformization iff E is smooth. Moreover, we compute the minimal definable complexity of counterexamples when E is not smooth. Our counterexamples use category, measure, and Ramsey-theoretic methods.
We also consider “local” dichotomies for such pairs (E,P). We give two new proofs of a dichotomy of Miller in the case where P has countable sections, the first using Miller’s (G0,H0) dichotomy and Lecomte’s ℵ0-dimensional G0 dichotomy, and the second using a new ℵ0-dimensional analogue of the (G0,H0) dichotomy. We also prove anti-dichotomy results for the “large section” case. We discuss the “Kσ section” case, which is still open.
This is joint work with Alexander Kechris.
Information: See the seminar webpage.
Vienna Research Seminar in Set Theory
Time: Thursday, 16 May, 11:30-13:00 CEST
Speaker: O. Zindulka, Czech Technical University Prague
Title: Combinatorics of Uniform Covers
Abstract: We look at diagonalization properties for sequences of various flavors of uniform covers of separable metric spaces and we describe them with game-theoretic and Ramsey-like partition properties. Applications include strong measure zero, null-additive and meager-additive sets in Polish groups, Menger-bounded spaces etc.
Some highlights: a link to fractal measures and how it can help with calculation of cardinal invariants; Galvin-Mycielski-Solovay Theorem in various contexts;a solution to a Scheepers problem regarding products of strong measure zero spaces.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 16 May, 15:00 – 15:50 CEST
Speaker: R. Sklinos, Chinese Academy of Sciences, Beijing
Title: First-order sentences in random groups
Abstract: Gromov in his seminal paper introducing hyperbolic groups claimed that a “typical” finitely presented group is hyperbolic. His statement can be made rigorous in various natural ways. The model of randomness that is preferentially focused on is Gromov’s density model, as it allows a fair amount of flexibility. In this model a random group is hyperbolic with overwhelming probability. In a different line of thought, Tarski asked whether all non abelian free groups share the same first-order theory (in the language of groups). This question proved very hard to tackle and only after more than 50 years Sela and Kharlampovich-Myasnikov answered the question positively. Combining the two, J. Knight conjectured that a first-order sentence holds with overwhelming probability in a random group if and only if it is true in a no abelian free group.
In joint work with O. Kharlampovich we answer the question positively for universal-existential sentences.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
6 – 12 May
Hebrew University Set Theory Seminar
Time: Wednesday, 8 May, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: Shimon Garti
Title: Unbalanced polarized relations
Abstract: Erdos, Hajnal and Rado asked whether a prescribed unbalanced polarized relation holds at a successor of a singular cardinal of countable cofinality. We shall force a negative answer, starting from a measurable cardinal in the ground model. The result can be pushed down to aleph-omega.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Set Theory Seminar
Time: Wednesday, 8 May, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 8 May, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker: Anton Bernshteyn, Georgia Institute of Technology
Title: Fractional graph theory in the Borel setting
Abstract: Fractional graph theory studies modifications of classical graph-theoretic problems (colorings, matchings, etc.) in which the answer is no longer required to be an integer. The study of fractional graph theory in the Borel setting was initiated by Meehan in 2018. In this talk, we will discuss “geometric” assumptions under which Borel and ordinary fractional combinatorics coincide. This is joint work with Felix Weilacher.
Information: See the seminar webpage.
Toronto Set Theory Seminar
Time: Friday, 10 May, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
29 April – 5 May
Hebrew University Set Theory Seminar
Time: Wednesday, 1 May, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 1 May, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 1 May, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker: Robert Simon, London School of Economics and Political Science
Title: Paradoxical decompositions and colouring rules
Abstract: A colouring rule is a way to colour the points x of a probability space according to the colours of finitely many measures preserving tranformations of x. The rule is paradoxical if the rule can be satisfied a.e. by some colourings, but by none whose inverse images are measurable with respect to any finitely additive extension for which the transformations remain measure preserving. We demonstrate paradoxical colouring rules defined via u.s.c. convex valued correspondences (if the colours b𝑏 and c𝑐 are acceptable by the rule than so are all convex combinations of b𝑏 and c𝑐). This connects measure theoretic paradoxes to problems of optimization and shows that there is a continuous mapping from bounded group-invariant measurable functions to itself that doesn’t have a fixed point (but does has a fixed point in non-measurable functions).
Information: See the seminar webpage.
Vienna Research Seminar in Set Theory
Time: Thursday, 2 May, 11:30-13:00 CEST
Speaker: C. B. Switzer, Universität Wien
Title: Baumgartner’s Axiom and Cardinal Characteristics: A Sparse Look at Dense Sets of Reals II
Abstract: Mini-course (25.04.2024 – 16.05.2024, 3 lectures) – 2nd lecture:
Given a cardinal κ, a set of reals A⊆R is κ-dense if its intersection with any open interval has size κ. Baumgartner’s axiom (BA) — proved consistent by Baumgartner in 1973 — states that all ℵ1-dense sets of reals are order isomorphic with the induced linear order from R. This is the most straightforward generalization to the uncountable of Cantor’s proof that all countable dense linear orders without endpoints are order isomorphic. BA has variations to other topological spaces — given a topological space X, a subset A⊆X is κ-dense if its intersection with each non-empty open subset has size κ. The axiom BA(X) states that given any two ℵ1-dense subsets of X, say A and B, there is an autohomeomorphism of X mapping A onto B. In this parlance BA is equivalent to BA(R). Surprisingly BA is not equivalent to BA(Rn) for any finite 1<n<ω. In fact BA does not follow from Martin’s Axiom (Abraham-Rubin-Shelah) though BA(Rn) does (in fact from p>ℵ1) for each n>1 (Steprāns-Watson).
In these three lectures I will discuss these ideas and some related ones including the question of when BA(X) implies BA(Y) for Polish spaces X and Y. Central to these questions are the role of cardinal characteristics including the celebrated theorem of Todorčević that BA implies b>ℵ1 as well as a recent, higher dimensional analogue of this result that for any n<ω BA(Rn) implies b>ℵ1 (S.-Steprāns). There are many beautiful open problems in this area and I plan to make discussing them a focal point of the talks. The talks will start slowly and should be accessible to students. Time permitting, the final talk will include some new results. If and when these results are presented, they are joint work with Juris Steprāns.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Cross-Alps Logic Seminar
Time: Friday, 3 May, 16.00-17.00 CEST
Speaker: S. Unger, University of Toronto
Title: Iterated ultrapower methods
Abstract: We develop some of the basic theory of iterated ultrapowers and survey some old and new results in singular cardinal combinatorics whose proofs can be phrased in terms of them.
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
New York Set Theory Seminar
Time: Friday, 3 May, 12.30-1.45pm New York time (18.30-20.45 CEST)
Speaker: Spencer Unger, University of Toronto
Title: Iterated ultrapower methods in analysis of Prikry type forcing
Abstract: We survey some old and new results in singular cardinal combinatorics whose proofs can be phrased in terms of iterated ultrapowers and ask a few questions.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 3 May, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
22 – 28 April
Hebrew University Set Theory Seminar
Time: Wednesday, 24 April, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 24 April, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Vienna Research Seminar in Set Theory
Time: Thursday, 25 April, 11:30-13:00 CEST
Speaker: C. B. Switzer, Universität Wien
Title: Baumgartner’s Axiom and Cardinal Characteristics: A Sparse Look at Dense Sets of Reals
Abstract: Mini-course (25.04.2024 – 16.05.2024, 3 lectures) – 1th lecture:
Given a cardinal κ, a set of reals A⊆R is κ-dense if its intersection with any open interval has size κ. Baumgartner’s axiom (BA) — proved consistent by Baumgartner in 1973 — states that all ℵ1-dense sets of reals are order isomorphic with the induced linear order from R. This is the most straightforward generalization to the uncountable of Cantor’s proof that all countable dense linear orders without endpoints are order isomorphic. BA has variations to other topological spaces — given a topological space X, a subset A⊆X is κ-dense if its intersection with each non-empty open subset has size κ. The axiom BA(X) states that given any two ℵ1-dense subsets of X, say A and B, there is an autohomeomorphism of X mapping A onto B. In this parlance BA is equivalent to BA(R). Surprisingly BA is not equivalent to BA(Rn) for any finite 1<n<ω. In fact BA does not follow from Martin’s Axiom (Abraham-Rubin-Shelah) though BA(Rn) does (in fact from p>ℵ1) for each n>1 (Steprāns-Watson).
In these three lectures I will discuss these ideas and some related ones including the question of when BA(X) implies BA(Y) for Polish spaces X and Y. Central to these questions are the role of cardinal characteristics including the celebrated theorem of Todorčević that BA implies b>ℵ1 as well as a recent, higher dimensional analogue of this result that for any n<ω BA(Rn) implies b>ℵ1 (S.-Steprāns). There are many beautiful open problems in this area and I plan to make discussing them a focal point of the talks. The talks will start slowly and should be accessible to students. Time permitting, the final talk will include some new results. If and when these results are presented, they are joint work with Juris Steprāns.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 25 April, 15:00 – 15:50 CEST
Speaker: J. Lopez-Abad, UNED Barcelona
Title: Banach spaces as metric model-theoretical structures
Abstract: Banach spaces are a reach family of metric model structures. We will discuss this in particular focussing on omega-categoricity, ultrahomogeneity and extreme amenability, where also combinatorics plays a crucial role.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Toronto Set Theory Seminar
Time: Friday, 26 April, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
15 – 21 April
CMU Core Model Seminar
Time: Tuesday, 16 April, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)
Speaker: Grigor Sargsyan, Polish Academy of Sciences
Title: The Komitas Model (part 3)
Abstract: We will introduce an inner model of a determinacy model that we call the Komitas Model. It is a type of Chang Model, it is built assuming AD^+ and it has the form L((HOD|gamma)^omega). We will show how to derive from hod mice Komitas models with rich combinatorial structure. We will then show how this structure can be transferred to models of ZFC that have combinatorially rich H_{omega_3}, H_{omega_4} and etc. For example, given a natural number n>1, we will obtain a model in which square(omega_i) fails for all i in the interval [2, n].
In these models, various K^c constructions fail to converge, and the construction of the models requires a Woodin cardinal that is a limit of Woodin cardinals. This has the consequence, via a result of Jensen-Schimmerling-Schindler-Steel, that the ZFC alone does not prove that various types of K^c constructions converge. We will also discuss other applications. This is a joint work with Paul Larson and Douglas Blue.
Komitas was an Armenian composer of folk music. He had a tragic life as a survivor of the Armenian Genocide of 1915.
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 16 April, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker: Doug Blue (University of Pittsburgh)
Title: Berkeley cardinals and AD
Abstract: Large cardinals beyond Choice are large cardinal axioms incompatible with Choice but not known to be inconsistent in ZF.
We will survey the Reinhardt and Berkeley hierarchies of such axioms, the implications their consistency would have for inner modeltheory, and recent theorems bearing on whether they are indeed consistent.
We will then describe joint work with Grigor Sargsyan which shows that Berkeley cardinal phenomena are ubiquitous assuming the Axiom of Determinacy and suggests that obtaining ZFC models of HOD-Berkeley cardinals by forcing is nontrivial.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 17 April, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 17 April, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Vienna Research Seminar in Set Theory
Time: Thursday, 18 April, 11:30-13:00 CEST
Speaker: R. Sullivan, Universität Münster
Title: Generic embeddings into Fraïssé structures
Abstract: Let M be a Fraïssé structure (eg the random graph), and let A be a countably infinite structure which is embeddable in M. If Mhas free amalgamation, then there exists a Katetov embedding of A into M: an embedding such that each automorphism of Aextends to an automorphism of M. Is this embedding “common” or “uncommon”?
To answer this, we investigate generic embeddings of A into M. An embedding of A into M is said to be generic if it lies in a comeagre set inside the Polish space Emb(A, M).
We will answer the following three questions:
– When are two embeddings of A into M generically isomorphic via an automorphism of M?
– When is A generically corigid (i.e. Aut(M/A) trival)?
– Let γ lie in Aut(A). When is γ generically isomorphic via an automorphism of M?
We will also discuss a wide range of examples in the context of these three questions.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 18 April, 15:00 – 15:50 CEST
Speaker: C. Agostini, TU Wien
Title: Countable spaces and realcompactness
Abstract: In this talk, we analyze the realcompactness number of countable spaces. We will show that, for every cardinal κ, there exists a countable crowded space X such that Exp(X)=κ if and only if p≤κ≤c. On the other hand, we show that a scattered space of weight κ has pseudocharacter at most κ in any compactification. This will allow us to calculate Exp(X) for an arbitrary (that is, not necessarily crowded) countable space. This is a joint work with Andrea Medini and Lyubomyr Zdomskyy.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
8 – 14 April
CMU Core Model Seminar
Time: Tuesday, 9 April, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)
Speaker: Grigor Sargsyan, Polish Academy of Sciences
Title: The Komitas Model (2/3)
Abstract: We will introduce an inner model of a determinacy model that we call the Komitas Model. It is a type of Chang Model, it is built assuming AD^+ and it has the form L((HOD|gamma)^omega). We will show how to derive from hod mice Komitas models with rich combinatorial structure. We will then show how this structure can be transferred to models of ZFC that have combinatorially rich H_{omega_3}, H_{omega_4} and etc. For example, given a natural number n>1, we will obtain a model in which square(omega_i) fails for all i in the interval [2, n].
In these models, various K^c constructions fail to converge, and the construction of the models requires a Woodin cardinal that is a limit of Woodin cardinals. This has the consequence, via a result of Jensen-Schimmerling-Schindler-Steel, that the ZFC alone does not prove that various types of K^c constructions converge. We will also discuss other applications. This is a joint work with Paul Larson and Douglas Blue.
Komitas was an Armenian composer of folk music. He had a tragic life as a survivor of the Armenian Genocide of 1915.
Information: Please email ernest Schimmerling in advance for the login.
Hebrew University Set Theory Seminar
Time: Wednesday, 10 April, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 10 April, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Renyi Institute Set Theory Seminar
Time: Thursday, 11 April, 10:30 – 12:00 CEST
Speaker: Alessandro Andretta
Title: A spray in $ \mathbb{R}^d $ is a subset with a point called center, such that every sphere with that center intersects the spray in a finite set. J. Schmerl introduced sprays when $ d = 2$, and he proved that $ 2^{\aleph_0 } \leq \aleph_n $ iff the plane can be covered with $ n + 2$ sprays with collinear centers.
We generalize this to all dimensions $d \geq 3$. In particular we show that $ 2^{\aleph_0 } \leq \aleph_n $ iff $ \mathbb{R}^3 $ can be covered with $ 2 n + 3 $ sprays such that their centers are coplanar and no three of them are collinear.
This is joint work with Ivan Izmestiev.
Information: The talks will be given in hybrid format. Please see the conference webpage for the login information.
Vienna Research Seminar in Set Theory
Time: Thursday, 11 April, 11:30-13:00 CEST
Speaker: J. M. Millhouse, Universität Wien
Title: Definable well-orderings of a large continuum (part 1)
Abstract: This is the first in a series of talks where I will be going over the
history and the more recent advancements in forcing techniques used to
produce models of set theory where the continuum is strictly greater
than \(\aleph_1\), a projective well-order of the reals.
In the first talk we will establish preliminaries, understand the
motivation for obtaining such models, and go over L. Harrington’s
initial 1977 construction. Subsequent talks will focus on some more
recent results, including applications of the techniques to the theory
of cardinal characteristics and the definability of various
combinatorial sets of reals.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 12 April, 12.30-1.45pm New York time (18.30-20.45 CEST)
Speaker: Boban Velickovic, University of Paris
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 12 April, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
1 – 7 April
CMU Core Model Seminar
Time: Tuesday, 2 April, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Grigor Sargsyan, Polish Academy of Sciences
Title: The Komitas Model (1/3)
Abstract: We will introduce an inner model of a determinacy model that we call the Komitas Model. It is a type of Chang Model, it is built assuming AD^+ and it has the form L((HOD|gamma)^omega). We will show how to derive from hod mice Komitas models with rich combinatorial structure. We will then show how this structure can be transferred to models of ZFC that have combinatorially rich H_{omega_3}, H_{omega_4} and etc. For example, given a natural number n>1, we will obtain a model in which square(omega_i) fails for all i in the interval [2, n].
In these models, various K^c constructions fail to converge, and the construction of the models requires a Woodin cardinal that is a limit of Woodin cardinals. This has the consequence, via a result of Jensen-Schimmerling-Schindler-Steel, that the ZFC alone does not prove that various types of K^c constructions converge. We will also discuss other applications. This is a joint work with Paul Larson and Douglas Blue.
Komitas was an Armenian composer of folk music. He had a tragic life as a survivor of the Armenian Genocide of 1915.
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 2 April, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Natasha Dobrinen, Notre Dame University
Title: Ramsey spaces of Fraisse structures
Abstract: The Galvin-Prikry theorem states that Borel subsets of the Baire space are Ramsey. Silver extended this to analytic sets, and Ellentuck gave a topological characterization of Ramsey sets in terms of the property of Baire in the Vietoris topology. We present work extending these theorems to several classes of countable homogeneous structures. An obstruction to exact analogues of Galvin-Prikry or Ellentuck is the presence of big Ramsey degrees. We will discuss how different properties of the structures affect which analogues have been proved. Presented is work of the speaker for structures with SDAP$^+$ and joint work with Zucker for binary finitely constrained FAP classes. A feature of the work with Zucker is showing that we can weaken one of Todorcevic’s four axioms guaranteeing a Ramsey space, and still achieve the same conclusion.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 3 April, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 3 April, 14:00-15:00 local time (15:00-16:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Cross-Alps Logic Seminar
Time: Friday, 5 April, 16.00-17.00 CET
Speaker: Luca Motto Ros, University of Torino
Title: Borel complexity of graph homomorphism
Abstract: tba
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
New York Set Theory Seminar
Time: Friday, 5 April, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Kameryn Williams, Bard College at Simon’s Rock
Title: Mediate cardinals
Abstract: In the late 1910s Bertrand Russell was occupied with two things: getting into political trouble for his pacifism and trying to understand the foundations of mathematics. His students were hard at work with him on this second occupation. One of those students was Dorothy Wrinch. In 1923 she gave a characterization of the axiom of choice in terms of a generalization of the notion of a Dedekind-finite infinite set. Unfortunately, her career turned toward mathematical biology and her logical work was forgotten by history.
This talk is part of a project of revisiting Wrinch’s work from a modern perspective. I will present the main result of her 1923 paper, that AC is equivalent to the non-existence of what she termed mediate cardinals. I will also talk about some new independence results. The two main results are: (1) the smallest κ for which a κ-mediate cardinal exists can consistently be any regular κ and (2) the collection of regular κ for which exact κ-mediate cardinals exist can consistently be any class.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 5 April, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Daniel Calderon, University of Toronto
Title: Borel’s conjecture and meager-additive sets
Abstract: Strong measure zero sets were introduced by Borel and have been studied since the beginning of the previous century. Borel conjectured that every strong measure zero set of real numbers must be countable. A few years later, Sierpiński proved that if the continuum hypothesis is assumed, an uncountable strong measure zero set of reals exists. Nevertheless, the question about the relative consistency of Borel’s conjecture remained open until 1976 when Laver, in a ground-breaking paper, constructed a model of set theory in which every strong measure zero set of reals is countable.
A result of Galvin, Mycielski, and Solovay provides a characterization of Borel’s strong nullity in terms of an algebraic (or translation-like) property for subsets of the real line. By means of this characterization, a strengthening of strong nullity, meager-additivity, appeared on the scene. Meager-additivity, as well as other smallness notions for subsets of the real line have received considerable attention in recent years. A 1993 question due to Bartoszyński and Judah asks whether strong nullity and meager-additivity have a very rigid relationship, in the following sense:
Question (Bartoszyński–Judah, 1993): Suppose that every strong measure zero set of reals is meager-additive. Does Borel’s conjecture follow?
In this talk, I’ll provide a proof of the relative consistency with ZFC of the statement: every strong measure zero subset of the real line is meager-additive and there are uncountable strong measure zero sets (i.e., Borel’s conjecture fails), giving a negative answer to the question above.
Information: Please see the conference webpage for the login information.
25 – 31 March
CMU Core Model Seminar
Time: Tuesday, 26 March, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Nam Trang, University of North Texas
Title: Ideals and Strong Axioms of Determinacy (part 3)
Abstract: We present the main ideas behind the proof of the equiconsistency of the theories:
(1) ZF + AD_R + \Theta is regular.
(2) ZFC + CH + there is an \omega_1-dense ideal on \omega_1.
(3) ZFC + the nonstationary ideal on P_{\omega_1}(R) is strong and pseudo-homogeneous.
This resolves a long-standing open problem asked by W.H. Woodin in the 1990’s. In the first talk, we discuss some history related to this problem and the general program in descriptive inner model theory that aims to calibrate the consistency strength of theories like the above. In the next two talks, we outline some main ideas behind the proof: the forcing construction that shows (1) is an upper bound (consistency-wise) of (2) and (3), and the core model induction that shows (2), (3) are upper bounds for (1).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 26 March, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Alejandro Poveda Ruzafa, Harvard University
Title: On $C^{(1)}$-supercompactness
Abstract: A cardinal $\kappa$ is called $C^{(1)}$-supercompact if for each cardinal $\lamba>\kappa$ there is an elementary embedding $j:V\rightarrow M$ with $\operatorname{crit}(j)=\kappa$, $j(\kappa)>\lambda$, $M^{\lambda}\subseteq M$, and $j(\kappa)$ strong limit (Bagaria, 2012). In this talk I would like to discuss the relationship between this notion and classical supercompactness. Our main result is the consistency (with all known large cardinals) that every supercompact cardinal is $C^{(1)}$-supercompact. This problem is tightly connected with the following inner-model-theoretic question: Suppose that $\kappa$ is a cardinal carrying an elementary embedding $j:V\rightarrow M$ with $\operatorname{crit}(j)=\kappa$, $M^{\kappa}\subseteq M$ and $j(\kappa)$ strong limit — must $\kappa$ be superstrong with target $j(\kappa)$? On the one hand, Woodin has conjectured (2018) that under $V=\mathrm{Ultimate-}L$” the above has an affirmative answer and, as a result, that every $C^{(1)}$-supercompact cardinal is a limit of supercompacts. On the other hand, our theorem shows that the opposite configuration is consistent even with $I_0$ cardinals.
If time permits I will also present some recent results connecting supercompact and extendible cardinals with Woodin’s HOD conjecture. Part of these latter results are joint work with Gabe Goldberg.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Speaker: Saharon Shelah
Title: Corrected Iteration (part 5)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 27 March, 14:00-15:00 local time (15:00-16:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
18 – 24 March
CMU Core Model Seminar
Time: Tuesday, 19 March, 1:30 – 3:00pm Pittsburgh time (18:30 – 20:00 CET)
Speaker: Nam Trang, University of North Texas
Title: Ideals and Strong Axioms of Determinacy (part 2)
Abstract: We present the main ideas behind the proof of the equiconsistency of the theories:
(1) ZF + AD_R + \Theta is regular.
(2) ZFC + CH + there is an \omega_1-dense ideal on \omega_1.
(3) ZFC + the nonstationary ideal on P_{\omega_1}(R) is strong and pseudo-homogeneous.
This resolves a long-standing open problem asked by W.H. Woodin in the 1990’s. In the first talk, we discuss some history related to this problem and the general program in descriptive inner model theory that aims to calibrate the consistency strength of theories like the above. In the next two talks, we outline some main ideas behind the proof: the forcing construction that shows (1) is an upper bound (consistency-wise) of (2) and (3), and the core model induction that shows (2), (3) are upper bounds for (1).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 19 March, 3:30 – 4:30pm Pittsburgh time (20:30 – 21:30 CET)
Speaker: Denis Hirschfeldt, University of Chicago
Title: Reductions between problems in reverse mathematics and computability theory
Abstract: Many mathematical principles can be stated in the form “for all X such that C(X) holds, there is a Y such that D(X,Y) holds”, where X and Y range over second-order objects, and C and D are arithmetic conditions. We can think of such a principle as a problem, where an instance of the problem is an X such that C(X) holds, and a solution to this instance is a Y such that D(X,Y) holds. I will discuss notions of reducibility between such problems coming from the closely-related perspectives of reverse mathematics and computability theory.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Speaker: Saharon Shelah
Title: Corrected Iteration (part 4)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 21 March, 11:30-13:00 CET
Speaker: Martina Iannella, TU Wien
Title: (Piecewise) convex embeddability on linear orders
Abstract: Given a nonempty set L of linear orders, we say that the linear order L is L-convex embeddable into the linear order L′ if it is possible to partition L into convex sets, indexed by some element of L, which are isomorphic to convex subsets of L′ ordered in the same way. This notion generalizes convex embeddability and (finite) piecewise convex embeddability, which arise from the special cases L={1} and L=Fin. In this talk we focus on the behaviour of these relations on the set of countable linear orders, first characterising when they are transitive, and hence a quasi-order. We then look at some combinatorial properties and complexity (with respect to Borel reducibility) of these quasi-orders. Finally, we analyse their extension to uncountable linear orders.
The presented results stem from joint work with Alberto Marcone, Luca Motto Ros, and Vadim Weinstein.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 21 March, 15:00 – 15:50 CET
Speaker: K. Krupiński, University of Wrocław
Title: On some applications of model theory and topological dynamics to additive combinatorics
Abstract: Model theory is a fast growing branch of mathematical logic with deep interactions with algebra, algebraic geometry, combinatorics, and, more recently, topological dynamics. I will focus on a few interactions with topological dynamics, and applications to additive combinatorics.
I will discus type-definable components of definable groups, which lead to model-theoretic descriptions of Bohr compactificatios of groups and rings, and also to so-called locally compact models of approximate subgroups and subrings which in turn are crucial to get structural or even classification results about approximate subgroups and subrings. I will discuss my result that each approximate subring has a locally compact model, and mention some structural applications. In contrast to approximate subrings, not every approximate subgroup has a locally compact model. However, Ehud Hrushovski showed that instead it has such a model in a certain generalized sense (with morphisms replaced by quasi-homomorphisms). In order to do that, he introduced and developed local logics and definability patterns. In my recent paper with Anand Pillay, we gave a shorter and simpler construction of a generalized locally compact model, based on topological dynamics methods in a model-theoretic context. I will briefly discuss it, if time permits.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 22 March, 12.30-1.45pm New York time (17.30-19.45 CET)
Speaker: Arthur Apter, CUNY
Title: A choiceless answer to a question of Woodin
Abstract: In a lecture presented in July 2023, Moti Gitik discussed the following question from the 1980s due to Woodin, as well as approaches to its solution and why it is so difficult to solve: Question: Assuming there is no inner model of ZFC with a strong cardinal, is it possible to have a model M of ZFC such that M⊨’2ℵω>ℵω+2 and 2ℵn=ℵn+1 for every n<ω’, together with the existence of an inner model N∗⊆M of ZFC such that for the γ,δ so that γ=(ℵω)M and δ=(ℵω+3)M, N∗⊨’γ is measurable and 2γ≥δ’?
I will discuss how to find answers to this question, if we drop the requirement that M satisfies the Axiom of Choice. I will also briefly discuss the phenomenon that on occasion, when the Axiom of Choice is removed from consideration, a technically challenging question or problem becomes more tractable. One may, however, end up with models satisfying conclusions that are impossible in ZFC.
Reference: A. Apter, ‘A Note on a Question of Woodin’, Bulletin of the Polish Academy of Sciences (Mathematics), volume 71(2), 2023, 115–121.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 22 March, 1.30-3.00pm Toronto time (18.30-20.00 CET)
Speaker: Frank Tall, University of Toronto
Title: Grothendieck spaces
Abstract: In 1952 Grothendieck proved a result connecting the question of when countably compact subspaces of certain function spaces are compact with the ability to interchange double limits, as is often done in Analysis. Iovino and colleagues connected the interchange of double limits to questions of definability of pathological Banach spaces. In his recent lecture in this seminar, he connected that interchange to questions in Machine Learning. With my recent Ph.D. student, Clovis Hamel, I extended Iovino’s work to deal with such definability in not necessarily compact logics. Previously I had answered questions of Arhangel’skii concerning generalizations of Grothendieck’s work by showing they were undecidable. Today I will speak about the topology involved in both of these endeavours.
Information: Please see the conference webpage for the login information.
11 – 17 March
CMU Core Model Seminar
Time: Tuesday, 12 March, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Nam Trang, University of North Texas
Title: Ideals and Strong Axioms of Determinacy
Abstract: We present the main ideas behind the proof of the equiconsistency of the theories:
(1) ZF + AD_R + \Theta is regular.
(2) ZFC + CH + there is an \omega_1-dense ideal on \omega_1.
(3) ZFC + the nonstationary ideal on P_{\omega_1}(R) is strong and pseudo-homogeneous.
This resolves a long-standing open problem asked by W.H. Woodin in the 1990’s. In the first talk, we discuss some history related to this problem and the general program in descriptive inner model theory that aims to calibrate the consistency strength of theories like the above. In the next two talks, we outline some main ideas behind the proof: the forcing construction that shows (1) is an upper bound (consistency-wise) of (2) and (3), and the core model induction that shows (2), (3) are upper bounds for (1).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 12 March, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Filippo Calderoni, Rutgers University
Title: Condensation and left-orderable groups
Abstract: In this talk we will discuss the phenomenon of condensation for group actions. We will show how condensation is used to study the descriptive complexity of some countable Borel equivalence relations occurring in group theory. In particular, we will analyze the conjugacy orbit equivalence relation for the solvable Baumslag-Solitar groups on their space of left-orders. This is joint work with Adam Clay.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 13 March, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Saharon Shelah
Title: Corrected Iteration (part 3)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 14 March, 11:30-13:00 CET
Speaker: David Schrittesser, Harbin Institute of Technology
Title: How economists forgot about multi-player utility and how we remembered
Abstract: This is all joint work with Ali M. Khan (Johns Hopkins) and Paul Arthur Pedersen (CUNY).
Game theory as practiced by economists is often couched in a setting where players pick strategies, and then a utility function tells them who has which pay off (the so-called “normal form” of a game). For two person games, an important special case is the zero sum game: the case where pay offs always sum to zero. Aumann, the sixties, defined “strictly competitive games”, two player games in which what is good for one player is bad for the other. Aumann frequently stated that this is the same class as the zero sum games—for an appropriate choice of utility function (and provided the players strategy spaces are closed under mixing).
We claim that Aumann must have known this because he knew the multidimensional theory of utility. But then in 2009, Adler, Daskalakis and Papadimitriou gave a non-trivial proof of the fact claimed by Aumann, for finite games, claiming that no such proof exists in the literature. This was generalized in 2023 by Raimondo to games where the set of strategies available to each player is an appropriate set of probability measures on [0,1] (or if you’re feeling fancy, on a standard Borel space).
In this talk, I shall show what Aumann and others must already have been aware of, but what has apparently been forgotten in the meantime: That these results, and more general ones, follow easily from the theory of mutlidimensional utility developed in the 60ies and early 70ies by Fishburn, Roberts, and others.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 14 March, 15:00 – 15:50 CET
Speaker: A. Kwiatkowska, Universität Münster
Title: Projective Fraisse limits of trees
Abstract: We continue the study of projective Fraisse limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. We focus on particular classes of epimorphisms such as monotone, confluent or simple confluent, which are adaptations to graphs of monotone or confluent maps from continuum theory. As the topological realizations of the projective Fraisse limits we obtain the dendrite D3 the Mohler-Nikiel universal dendroid, as well as new, interesting compact connected spaces (continua) for which we do not yet have topological characterizations.
The talk is based on joint work with Charatonik, Roe, Yang.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 15 March, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Chris Lambie-Hanson, Czech Academy of Sciences
Title: Squares, ultrafilters and forcing axioms
Abstract: A uniform ultrafilter U over a cardinal κ>ω1 is called indecomposable if, whenever λ<κ and f:κ→λ, there is a set X∈U such that f[X] is countable. Indecomposability is a natural weakening of κ-completeness and has a number of implications for, e.g., the structure of ultraproducts. In the 1980s, Sheard answered a question of Silver by proving the consistency of the existence of an inaccessible but not weakly compact cardinal carrying an indecomposable ultrafilter. Recently, however, Goldberg proved that this situation cannot hold above a strongly compact cardinal: If λ is strongly compact and κ≥λ carries an indecomposable ultrafilter, then κ is either measurable or a singular limit of countably many measurable cardinals. We prove that the same conclusion follows from the Proper Forcing Axiom, thus adding to the long list of statements first shown to hold above a strongly compact or supercompact cardinal and later shown also to follow from PFA. Time permitting, we will employ certain indexed square principles to prove that our results are sharp. This is joint work with Assaf Rinot and Jing Zhang.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 15 March, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Frank Tall, University of Toronto
Title: An undecidable extension of Morley’s theorem on the number of countable models
Abstract: Joint work with Christopher J. Eagle, Clovis Hamel, Sandra Müller.
We show that Morley’s theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, large cardinals, and Inner Model Theory.
Information: Please see the conference webpage for the login information.
4 – 10 March
Hebrew University Set Theory Seminar
Time: Wednesday, 6 March, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Saharon Shelah
Title: Corrected Iteration (part 2)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 7 March, 11:30-12:00 CET
Speaker: S. Horvath, ETH Zürich and A. F. Uribe Zapata, TU Wien
Title: Magic Sets
Abstract: A Magic Set is a set M of reals with the property that for all nowhere constant, continuous functions f and g on the reals it holds that f[M]⊆g[M] implies f=g.
I will cover some of the basic results on magic sets and introduce magic forcing — a forcing notion that adds a new magic set to the ground model.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 7 March, 12:00-13:00 CET
Speaker: A. F. Uribe Zapata, TU Wien
Title: A general theory of iterated forcing using finitely additive measures
Abstract: Saharon Shelah in 2000 introduced a finite-support iteration using finitely additive measures to prove that, consistently, the covering of the null ideal may have countable cofinality. In 2019, Jakob Kellner, Saharon Shelah, and Anda R. Tănasie achieved some new results and applications using such iterations.
In this talk, based on the works mentioned above, we present a general theory of iterated forcing using finitely additive measures, which was developed in the speaker’s master’s thesis. For this purpose, we introduce two new notions: on the one hand, we define a new linkedness property, which we call “FAM-linked” and, on the other hand, we generalize the idea of intersection number to forcing notions, which justifies the limit steps of our iteration theory. Finally, we show a new separation of the left-side of Cichoń’s diagram allowing a singular value.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 7 March, 15:00 – 15:50 CET
Speaker: E. Kaplan, McMaster University, Hamilton
Title: Hilbert polynomials for finitary matroids
Abstract: Eventual polynomial growth is a common theme in combinatorics and commutative algebra. The quintessential example of this phenomenon is the Hilbert polynomial, which eventually coincides with the linear dimension of the graded pieces of a finitely generated module over a polynomial ring.
A later result of Kolchin shows that the transcendence degree of certain field extensions of a differential field is eventually polynomial.
More recently, Khovanskii showed that for finite subsets A and B of a commutative semigroup, the size of the sumset A+tB is eventually polynomial in t.
I will present a common generalization of these three results in terms of finitary matroids (also called pregeometries). I’ll discuss other instances of eventual polynomial growth (like the Betti numbers of a simplicial complex) as well as some applications to bounding model-theoretic ranks.
This is joint work with Antongiulio Fornasiero.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 8 March, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Jonathan Osinski, Univeristy of Hamburg
Title: Model Theory of class-sized logics
Abstract: We consider logics in which the collection of sentences over a set-sized vocabulary can form a proper class. The easiest example of such a logic is L∞∞, which allows for disjunctions and conjunctions over arbitrarily sized sets of formulas and quantification over strings of variables of any infinite length. Model theory of L∞∞ is very restricted. For instance, it is inconsistent for it to have nice compactness or Löwenheim-Skolem properties. However, Trevor Wilson recently showed that the existence of a Löwenheim-Skolem-Tarski number of a certain class-sized fragment of L∞∞is equivalent to the existence of a supercompact cardinal, and various other related results. We continue this work by considering several appropriate class-sized logics and their relations to large cardinals. This is joint work with Trevor Wilson.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 8 March, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Clement Yung, University of Toronto
Title: Weak A2 Spaces and Ramsey Games
Abstract: We introduce the notion of a weak A2 space, which generalises topological Ramsey spaces and countable vector spaces. We shall show that in all topological Ramsey spaces, every set is Kastanas Ramsey iff Ramsey. If time permits, I’ll discuss how Kastanas Ramsey sets are related to coanalytic sets, and to strategically Ramsey sets (introduced by Rosendal) studied on countable vector spaces.
Information: Please see the conference webpage for the login information.
26 February – 3 March
CMU Logic Seminar
Time: Tuesday, 27 February, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Andrew Marks, UC Berkeley
Title: The recursive compression method for proving undecidability
Abstract: We discuss a technique called recursive compression for proving undecidability results. The method has developed independently in mathematics and theoretical computer science, and gives a way of showing some decision problem is undecidable by reducing the halting problem to it. Recursive compression was used by Durand, Romashchenko, and Chen in 2008 to give an alternate proof that the Wang tiling problem is undecidable. In quantum information theory, recursive compression was used by Ji, Natarajan, Vidick, Wright, and Yuen in 2020 to prove the MIP*=RE result that the halting problem is reducible to approximating the quantum value of a nonlocal game.
We formulate a general recursive compression lemma which abstracts the technique used in these applications. We also prove a converse of the recursive compression lemma showing that the halting problem is polytime reducible to an r.e. language if and only if there is a recursive compression proof. Finally, we generalize the recursive compression lemma throughout the arithmetical hierarchy, giving a way to show that a language is $\Sigma^0_k$-hard. This is joint work with Seyed Sajjad Nezhadi and Henry Yuen.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 28 February, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Saharon Shelah
Title: Corrected Iteration (part 1)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Cross-Alps Logic Seminar
Time: Friday, 1 March, 16.00-17.00 CET
Speaker: S. Henry, University of Ottawa
Title: Higher categorical language
Abstract: tba
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
19 – 25 February
CMU Core Model Seminar
Time: Tuesday, 20 February, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Obrad Kasum, Université Paris Cité
Title: Local definability of HOD in L(R), part 2
Abstract: In the first talk, I will gave an overview of the topic of study of HOD of L(R) in terms of Core Model Theory. In the second talk, I will present my recent result in this area which shows that HOD||η^{+HOD} is locally definable from HOD||η for all HOD-cardinals η∈[δ^2_1,Θ).
Information: Please email ernest Schimmerling in advance for the login.
Hebrew University Set Theory Seminar
Time: Wednesday, 7 February, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Possible and impossible pairs of compactness principles (part 5)
Abstract: In this sequence of talks I will discuss the challenges and the few known obstacles for obtaining interesting combinatorial reflection principles at a pair of cardinals.
I plan to talk about two main cases: Chang’s Conjecture and the tree property.
We will start by recalling some basic facts about the generalized Chang’s Conjecture. I will start by showing the consistency of a single instance of (higher) CC from a huge cardinal (in the gapless case) or from a supercompact cardinal (in the gapped case). I will describe the limitations on CC cases under GCH.
Then, I will describe how to get a global version of Chang’s Conjecture and show a ZFC theorem limiting pairs of consistent cases of CC.
I will show how the methods for obtaining the tree property at the successor of a singular cardinal resembles the ones for getting CC (to the extent that it is unknown how to get the tree property without CC), and discuss the limitations of the current technology, including a conjectural impossible pair.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Toronto Set Theory Seminar
Time: Friday, 23 February, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Cesar Corral, York University
Title: MAD families with pseudocompact hyperspaces
Abstract: Pseudocompactness of hyperspaces was studied by J. Ginsburg, who asked whether there is a relationship between the pseudocompactness of X^\omega and the hyperspace exp(X) for a topological space X. For an almost disjoint family \mathcal{A}, maximality is equivalent to pseudocompactness of \Psi(\mathcal{A}) and that of \Psi(\mathcal{A})^\omega. Hence J. Cao and T. Nogura asked whether some/every MAD family has a pseudocompact hyperspace.
Recently, the statement that every MAD family has a pseudocompact hyperspace was proved to be equivalent to the Novak or Baire number \mathfrak{n} being greater than \mathfrak{c}, however, not much more is known about the existence of MAD families with pseudocompact hyperspace. We will address this problem by showing many models and cardinal invariant assumptions that imply the existence of MAD families with pseudocompact hyperspace.
Information: Please see the conference webpage for the login information.
12 – 18 February
CMU Core Model Seminar
Time: Tuesday, 13 February, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Obrad Kasum, Vienna University of Technology
Title: Local definability of HOD in L(R), part 1
Abstract: In the first talk, I will give an overview of the topic of study of HOD of L(R) in terms of Core Model Theory. In the second talk, I will present my recent result in this area which shows that HOD||η^{+HOD} is locally definable from HOD||η for all HOD-cardinals η∈[δ^2_1,Θ).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 13 February, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Caroline Terry, Ohio State University
Title: Combinatorial complexity and regularity lemmas in groups
Abstract: Many tools have been developed in combinatorics to study global structure in finite graphs. One such tool is called Szemerédi’s regularity lemma, which gives a structural decomposition for any large finite graph. Beginning with work of Alon-Fischer-Newman, Lovász-Szegedy, and Malliaris-Shelah, it has been shown over the last 15 years that regularity lemmas can be used to detect structural dichotomies in graphs, and that these dichotomies have deep connections to model theory. In this talk, I present extensions of this type of result to arithmetic regularity lemmas, which are analogues of graph regularity lemmas, tailored to the study of combinatorial problems in finite groups.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 14 February, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Possible and impossible pairs of compactness principles (part 4)
Abstract: In this sequence of talks I will discuss the challenges and the few known obstacles for obtaining interesting combinatorial reflection principles at a pair of cardinals.
I plan to talk about two main cases: Chang’s Conjecture and the tree property.
We will start by recalling some basic facts about the generalized Chang’s Conjecture. I will start by showing the consistency of a single instance of (higher) CC from a huge cardinal (in the gapless case) or from a supercompact cardinal (in the gapped case). I will describe the limitations on CC cases under GCH.
Then, I will describe how to get a global version of Chang’s Conjecture and show a ZFC theorem limiting pairs of consistent cases of CC.
I will show how the methods for obtaining the tree property at the successor of a singular cardinal resembles the ones for getting CC (to the extent that it is unknown how to get the tree property without CC), and discuss the limitations of the current technology, including a conjectural impossible pair.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Toronto Set Theory Seminar
Time: Friday, 16 February, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Lucas O’Brien, University of Toronto
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
5 – 11 February
CMU Core Model Seminar
Time: Tuesday, 6 February, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Andreas Lietz, Vienna University of Technology
Title: Forcing “NS_{\omega_1} is \omega_1-Dense” from Large Cardinals (part 3)
Abstract:In three talks, I will present the main result from my thesis: Assuming there is a supercompact limit of supercompact cardinals, there is a semiproper forcing extension in which “NS_{\omega_1} is \omega_1-Dense” holds, i.e. there is a collection of $\omega_1$-many stationary sets, so that any stationary set contains one of them (modulo a nonstationary set). This property of the nonstationary ideal on $\omega_1$ implies saturation, but is much stronger. Previously, the only known way to get it to hold was to force with Q_{max} over L(R) assuming AD there, or over other canonical determinacy models (this is due to Woodin).
Our strategy will be to iterate a new version of the Aspero-Schindler (*)-forcing. One main challenge to overcome is that this forcing does in general not preserve stationary sets and we will prove an iteration theorem which allows such forcings without collapsing \omega_1.
In the end, we even get a new MM^{++}-style forcing axiom QM which implies “NS_{\omega_1} is \omega_1-Dense”.
Information: Please email ernest Schimmerling in advance for the login.
Hebrew University Set Theory Seminar
Time: Wednesday, 7 February, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Possible and impossible pairs of compactness principles (part 3)
Abstract: In this sequence of talks I will discuss the challenges and the few known obstacles for obtaining interesting combinatorial reflection principles at a pair of cardinals.
I plan to talk about two main cases: Chang’s Conjecture and the tree property.
We will start by recalling some basic facts about the generalized Chang’s Conjecture. I will start by showing the consistency of a single instance of (higher) CC from a huge cardinal (in the gapless case) or from a supercompact cardinal (in the gapped case). I will describe the limitations on CC cases under GCH.
Then, I will describe how to get a global version of Chang’s Conjecture and show a ZFC theorem limiting pairs of consistent cases of CC.
I will show how the methods for obtaining the tree property at the successor of a singular cardinal resembles the ones for getting CC (to the extent that it is unknown how to get the tree property without CC), and discuss the limitations of the current technology, including a conjectural impossible pair.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
New York Set Theory Seminar
Time: Friday, 9 February, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Tom Benhamou, Rutgers University
Title: Tukey-top ultrafilters under UA
Abstract: In the first part of the talk, we will provide some background and motivation to study the Glavin property. In particular, we will present a recently discovered connection between the Galvin property and the Tukey order on ultrafilters. This is a joint result with Natasha Dobrinen. In the second part, we will introduce several diamond-like principles for ultrafilters, and prove some relations with the Galvin property. Finally, we use the Ultrapower Axiom to characterize the Galvin property in the known canonical inner models. The second and third part is joint work with Gabriel Goldberg.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 9 February, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Khulod Almontashery, York University
Title: Proximal and Semi-proximal Spaces
Abstract: Jocelyn Bell introduced the notion of proximal spaces using uniformities to address problems related to uniform box products. A proximal space is a topological space X for which there exists a compatible uniformity such that Player I has a winning strategy in a specific two-player game of infinite length. I will give an exploratory introduction about the classes of spaces related to this game and share some recent joint work with Paul Szeptycki about the relationship of these spaces to normal topological spaces.
Information: Please see the conference webpage for the login information.
29 January – 4 February
CMU Core Model Seminar
Time: Tuesday, 30 January, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Andreas Lietz, Vienna University of Technology
Title: Forcing “NS_{\omega_1} is \omega_1-Dense” from Large Cardinals (part 2)
Abstract: In three talks, I will present the main result from my thesis: Assuming there is a supercompact limit of supercompact cardinals, there is a semiproper forcing extension in which “NS_{\omega_1} is \omega_1-Dense” holds, i.e. there is a collection of $\omega_1$-many stationary sets, so that any stationary set contains one of them (modulo a nonstationary set). This property of the nonstationary ideal on $\omega_1$ implies saturation, but is much stronger. Previously, the only known way to get it to hold was to force with Q_{max} over L(R) assuming AD there, or over other canonical determinacy models (this is due to Woodin).
Our strategy will be to iterate a new version of the Aspero-Schindler (*)-forcing. One main challenge to overcome is that this forcing does in general not preserve stationary sets and we will prove an iteration theorem which allows such forcings without collapsing \omega_1.
In the end, we even get a new MM^{++}-style forcing axiom QM which implies “NS_{\omega_1} is \omega_1-Dense”.
Information: Please email ernest Schimmerling in advance for the login.
Hebrew University Set Theory Seminar
Time: Wednesday, 31 January, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Possible and impossible pairs of compactness principles (part 2)
Abstract: In this sequence of talks I will discuss the challenges and the few known obstacles for obtaining interesting combinatorial reflection principles at a pair of cardinals.
I plan to talk about two main cases: Chang’s Conjecture and the tree property.
We will start by recalling some basic facts about the generalized Chang’s Conjecture. I will start by showing the consistency of a single instance of (higher) CC from a huge cardinal (in the gapless case) or from a supercompact cardinal (in the gapped case). I will describe the limitations on CC cases under GCH.
Then, I will describe how to get a global version of Chang’s Conjecture and show a ZFC theorem limiting pairs of consistent cases of CC.
I will show how the methods for obtaining the tree property at the successor of a singular cardinal resembles the ones for getting CC (to the extent that it is unknown how to get the tree property without CC), and discuss the limitations of the current technology, including a conjectural impossible pair.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Models and Sets Seminar
Time: Wednesday, 31 January, 14:00-15:00 local time (15:00-16:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
New York Set Theory Seminar
Time: Friday, 2 February, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Dima Sinapova, Rutgers University
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 2 February, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Jing Zhang, University of Toronto
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.
22 – 28 January
CMU Core Model Seminar
Time: Tuesday, 23 January, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Andreas Lietz, Vienna University of Technology
Title: Forcing “NS_{\omega_1} is \omega_1-Dense” from Large Cardinals, part 1
Abstract: In three talks, I will present the main result from my thesis: Assuming there is a supercompact limit of supercompact cardinals, there is a semiproper forcing extension in which “NS_{\omega_1} is \omega_1-Dense” holds, i.e. there is a collection of $\omega_1$-many stationary sets, so that any stationary set contains one of them (modulo a nonstationary set). This property of the nonstationary ideal on $\omega_1$ implies saturation, but is much stronger. Previously, the only known way to get it to hold was to force with Q_{max} over L(R) assuming AD there, or over other canonical determinacy models (this is due to Woodin).
Our strategy will be to iterate a new version of the Aspero-Schindler (*)-forcing. One main challenge to overcome is that this forcing does in general not preserve stationary sets and we will prove an iteration theorem which allows such forcings without collapsing \omega_1.
In the end, we even get a new MM^{++}-style forcing axiom QM which implies “NS_{\omega_1} is \omega_1-Dense”.
Information: Please email ernest Schimmerling in advance for the login.
Hebrew University Set Theory Seminar
Time: Wednesday, 24 January, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Possible and impossible pairs of compactness principles
Abstract: In this sequence of talks I will discuss the challenges and the few known obstacles for obtaining interesting combinatorial reflection principles at a pair of cardinals.
I plan to talk about two main cases: Chang’s Conjecture and the tree property.
We will start by recalling some basic facts about the generalized Chang’s Conjecture. I will start by showing the consistency of a single instance of (higher) CC from a huge cardinal (in the gapless case) or from a supercompact cardinal (in the gapped case). I will describe the limitations on CC cases under GCH.
Then, I will describe how to get a global version of Chang’s Conjecture and show a ZFC theorem limiting pairs of consistent cases of CC.
I will show how the methods for obtaining the tree property at the successor of a singular cardinal resembles the ones for getting CC (to the extent that it is unknown how to get the tree property without CC), and discuss the limitations of the current technology, including a conjectural impossible pair.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 25 January, 11:30-13:00 CET
Speaker: D. A. Mejía, Shizuoka University
Title: Forcing techniques for Cichoń’s Maximum VI: Forcing intersected with submodels
Abstract: Mini-course (30.11.2023-25.01.2024, 6 lectures)- 6th lecture:
We conclude the discussion about Boolean ultrapowers, and move to the technique of intersection with submodels, which is used to prove the consistency of Cichoń’s Maximum without using large cardinals.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 25 January, 15:00 – 15:50 CET
Speaker: Y. Khomskii, Amsterdam University College and Universität Hamburg
Title: Trees, Transcendence and Quasi-generic reals
Abstract: For a σ-ideal I on the Baire Space, a real is called quasi-generic over a model of set theory M if it avoids all Borel I-small sets coded in M. This is a natural generalisation of Cohen and Random reals due to Solovay, but only appeared as an explicit concept in the work of Brendle, Halbeisen and Löwe in 2005.
With the help of quasi-generic reals we can uncover connections between different phenomena in set theory of the reals, such as cardinal invariants, regularity properties for sets in the projective hierarchy, and forcing-theoretic properties of partial orders.
In this talk, I will first survey older results regarding this connection, built up using the uniform framework of idealized forcing due to Jindřich Zapletal. Then, I will survey recent developments in this area and mention several interesting problems that are still open.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Toronto Set Theory Seminar
Time: Friday, 26 January, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Shaun Allison, University of Toronto
Title: Lower bounds in potential Borel complexity (Part 2)
Abstract: Take your favorite classification problem in mathematics — isomorphism of graphs, homeomorphism of topological spaces, or conjugacy of measure preserving transformations — and most likely it can be modeled as the orbit equivalence relation of a Polish group acting on a Polish space. By using the tools of invariant descriptive set theory, we can measure the complexity of this orbit equivalence relation and conclude meaningful things about what kind of solution one can expect, if any, to the corresponding classification problem. One such measure of complexity is potential Borel complexity. We will develop the theory of this notion, and show how one can find elementary proofs of lower bound results using ideas of the Scott analysis and its generalization by Hjorth.
Information: Please see the conference webpage for the login information.
15 – 21 January
Vienna Research Seminar in Set Theory
Time: Thursday, 18 January, 11:30-13:00 CET
Speaker: D. A. Mejía, Shizuoka University
Title: Forcing techniques for Cichoń’s Maximum V: Boolean ultrapowers
Abstract: Mini-course (30.11.2023-25.01.2024, 6 lectures)- 5th lecture:
After finishing the discussion on ultrafilters and fams, we show how Boolean ultrapowers of compact cardinals can be used to force Cichoń’s Maximum.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 18 January, 15:00 – 15:50 CET
Speaker: A. Panagiotopoulos, Universität Wien
Title: The class and dynamics of α-balanced Polish groups
Abstract: A Polish group is TSI if it admits a two-side invariant metric. It is CLI if it admits complete and left-invariant metric. The class of CLI groups contains every TSI group but there are many CLI groups that fail to be TSI. In this talk we will introduce the class of α-balanced Polish groups where α-ranges over all countable ordinals. We will show that these classes completely stratify the space between TSI and CLI. We will also introduce “generic α-unbalancedness”: a turbulence-like obstruction to classification by actions of α-balanced Polish groups. Finally, for each α we will provide an action of an α-balanced Polish group whose orbit equivalence relation is not classifiable by actions of any β-balanced Polish group with β<α.
This is joint work with Shaun Allison.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Cross-Alps Logic Seminar
Time: Friday, 19 January, 16.00-17.00 CET
Speaker: C. Steinhorn, Vassar College
Title: O-minimality as a framework for tame mathematical economics. UNESCO World Logic Day Seminar
Abstract: This talk would focus on preference and utility theory in the context of o-minimal expansions of the ordered field of real numbers. We give a complete description of all preferences that can be defined in such a structure. We also raise questions about incomplete preferences in this context.
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
8 – 14 January
Vienna Research Seminar in Set Theory
Time: Tuesday, 9 January, 15:00 CET
Speaker: A. Cieślak, Wrocław University of Technology
Title: Cofinalities of tree ideals
Abstract: If T is a collection of trees on ωω, then we define the tree ideal t0 as a collection of these X⊂ωω such that each T∈T has a subtree S∈T which shares no branches with X. We will be interested in the cofinalities of tree ideals. Building on the work of Brendle, Khomskii, and Wohofsky, we will analyse the condition called “Incompatibility Shrinking Property”, which implies that cof(t0)>2ω. We will investigate under which assumptions this property is satisfied for two types of trees. These types are Laver and Miller trees which split positively according to some fixed ideal on ω. (Joint work with Arturo Martinez Celis.)
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Hebrew University Set Theory Seminar
Time: Wednesday, 10 January, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Menachem Magidor
Title: The Sigma^2_2 generic absoluteness problem (continued)
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 11 January, 11:30-13:00 CET
Speaker: D. A. Mejía, Shizuoka University
Title: Forcing techniques for Cichoń’s Maximum IV: FS iterations with measures and ultrafilters on the natural numbers
Abstract: Mini-course (30.11.2023-25.01.2024, 6 lectures)- 4th lecture:
We complete the proof of the consistency of the constellation for the left side of Cichoń’s diagram by showing how to preserve a strong witness for the unbounding number. However, this requires a modification of the iteration, and a new theory of iterations with measures and ultrafilters.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 11 January, 15:00 – 15:50 CET
Speaker: A. Lietz, TU Wien
Title: The Model Theoretic Covering Reflection Property
Abstract: The Covering Reflection Property holds at a cardinal κ if for every first order structure B in a countable language, there is some A of size <κ so that B can be covered with the ranges of elementary embeddings j:A→B. That is, for every b∈B, there is some a∈A and an elementary embedding j:A→B with j(a)=b. We discuss this property and isolate a new large cardinal notion strictly between almost huge and huge cardinals and show that the least cardinal exhibiting the Covering Reflection Property is exactly the least such large cardinal. Moreover, there is a natural correspondence between such large cardinals and strong forms of the Covering Reflection Property.
This is joint work with Joel D. Hamkins, Nai-Chung Hou and Farmer Schlutzenberg.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
6th World Logic Day Workshop, Renyi Institute
Time: Friday, 12 January, 12:55 – 19:00 CET
Speaker: Various
Title: Workshop celebrating the 6th World Logic Day
Information: The talks will be given in hybrid format. Please see the conference webpage for the login information.
European Set Theory Society 