Online activities 15 – 21 May

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Kobe Set Theory Seminar
Time: Monday, 15 May, 16:30 local time (09:30 CEST)
Speaker: Takehiko Gappo, TU Wien
Title: Chang models over derived models with supercompact measures (1/2)
Abstract: The relationship between the Axiom of Determinacy and supercompactness of ω1 has been studied by many people. In 1990’s, Woodin showed that assuming the existence of a proper class of Woodin limits of Woodin cardinals, a generalized Chang model satisfies “ADℝ + ω1 is supercompact.” Recently he also showed that the regularity of Θ in the model follows from determinacy of a long game of length ω1, which is, however, still unknown to be consistent. Based on these results, we conjecture that the following two theories are equiconsistent:
(1) ZFC + there is a Woodin limit of Woodin cardinals.
(2) ZF + ADℝ + Θ is regular + ω1 is supercompact.
Toward this conjecture, we construct a new model of the Axiom of Determinacy, called the Chang model over the derived model with supercompact measures. We then prove that it is consistent relative to a Woodin limit of Woodin cardinals that our model satisfies “ADℝ + Θ is regular + ω1 is < δ-supercompact for some regular cardinal δ > Θ.” This is joint work with Sandra Müller and Grigor Sargsyan. 　
Information: Please see the seminar webpage. This talk will be given in hybrid format. Please email Hiroshi Sakai for the zoom information in advance.

Baltic Set Theory Seminar
Time: Tuesday, 16 May, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
2. Paul Larson, A course on AD^+
Information: Please see the seminar webpage.

Leeds Models and Sets Seminar
Time: Wednesday, 17 May, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Will Boney, Texas State University
Title: Building generalized indiscernibles in nonelementary classes
Abstract: Generalized indiscernibles can be built in first-order theories by generalizing the combinatorial Ramsey’s Theorem to classes with more structure, which is an active area of study. Trying to do the same for infinitely theories (in the guise of Abstract Elementary Classes) requires generalizing the Erdos-Rado Theorem instead. We discuss various results about generalizations of the Erdos-Rado Theorem and techniques (including large cardinals and forcing) to build generalized indiscernibles.
Information: Please see the seminar webpage.

Caltech Logic Seminar
Time: Wednesday, 17 May, 12:00am-13:00pm Pacific time (21:00-22:00 CEST)
Speaker: Forte Shinko, UCLA
Title: The generic action of a free group on Cantor space is hyperfinite
Abstract: Let Γ be a countable free group. The set of continuous actions of Γ on Cantor space 2N admits a natural Polish topology, and hence we can talk about properties of the generic action. It was shown by Frisch-Kechris-Shinko-Vidnyánszky that the generic action is measure-hyperfinite, meaning that for every Borel probability measure μ on 2N, the action is hyperfinite modulo some μ-null set. Kwiatkowska showed using the methods of projective Fraïssé theory that there is only one generic action up to isomorphism. We use her techniques to investigate the generic action further, and in particular we show that the generic action is hyperfinite. This is joint work with Sumun Iyer.
Information: Please see the seminar webpage.

Renyi Institute Set Theory Seminar
Time: Thursday, 18 May, 10:30 – 12:00 CEST
Speaker: Amitayu Banerjee
Title: On a variant of Erdős–Dushnik–Miller theorem without the Axiom of Choice (AC)
Abstract: Theories: ZFC (Zermelo–Fraenkel set theory with the Axiom of Choice (AC)), ZF (Zermelo–Fraenkel set theory without AC), ZFA (ZF with the Axiom of Extensionality weakened to allow the existence of atoms).
Known informations:
In 1941, Ben Dushnik and Miller established the proposition “Every infinite graph contains either a countably infinite independent set or a clique with the same cardinality as the whole graph” in ZFC, and gave credit to Paul Erdős for the proof of the result for the case in which the cardinality of the graph is a singular cardinal. The above result is uniformly known as Erdős–Dushnik–Miller theorem.
Consider the following variant (abbreviated as EDM):  “Every uncountable graph contains either a countably infinite independent set or an uncountable clique”.  It is well-known that in ZFC, EDM implies the proposition “Any partially ordered set such that all of its antichains are finite and all of its chains are countable is countable” (we abbreviate by K) as well as the infinite Ramsey’s theorem (“Every infinite graph has either an infinite independent set or an infinite clique”).
In 1977, Andreas Blass studied the exact placement of the infinite Ramsey’s theorem in the hierarchy of weak forms of AC. In particular, he proved that the Boolean Prime Ideal Theorem (a weak form of AC) is independent of the infinite Ramsey’s theorem in ZF (i.e., there exists a ZF model where the Boolean Prime Ideal Theorem holds, but the infinite Ramsey’s theorem fails, and there exists a ZF model where the infinite Ramsey’s theorem holds, but the Boolean Prime Ideal Theorem fails) (see: https://doi.org/10.2307/2272866).
In 2021, I studied some relations of K with weak forms of AC. (see: arXiv:2009.05368v2; to appear).
In 2022, Eleftherios Tachtsis investigated the deductive strength of K without AC in more detail. Among several results, Tachtsis proved that DC_{\aleph_{1}} (Dependent Choices for \aleph_{1}, a weak form of AC stronger than Dependent Choices (DC)) implies K in ZF (see:  https://link.springer.com/article/10.1007/s00605-022-01751-9).
New Results: We study the exact placement of EDM in the hierarchy of weak forms of AC. In particular, we prove the following results (see arXiv:2211.05665v3):
1. The strength of EDM is strictly between  DC_{\aleph_{1}} and K in ZFA.
2. EDM is strictly stronger than the infinite Ramsey’s theorem in ZF (i.e., the infinite Ramsey’s theorem does not imply EDM in ZF).
3. The Boolean Prime Ideal Theorem is independent of EDM in ZFA (specifically, neither the Boolean Prime Ideal Theorem implies EDM in ZF, nor EDM implies the Boolean Prime Ideal Theorem in ZFA).
Finally, the speaker will state some open questions in this track.
Information: Please see the seminar webpage. This talk will be given in hybrid format.

Cross-Alps Logic Seminar
Time: Friday, 19 May, 16.00-17.00 CEST
Speaker: J. Duparc, Université de Lausanne
Title: tba
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.

CUNY Set Theory Seminar
Time: Friday, 19 May, 12:30pm New York time (18:15 CEST)
Speaker: Miha Habič, Bard College at Simon’s Rock
Title: Some old and new results on nonamalgamable forcing extensions
Abstract: Fixing some countable transitive model M of set theory, we can consider its generic multiverse, the family of all models obtainable from M by taking any sequence of forcing extensions and ground models. There is an attractive similarity between the generic multiverse and the Turing degrees, but the multiverse has the drawback (or feature?) that it contains nonamalgamable models, that is, models with no common upper bound, as was observed by several people, going back to at least Mostowski. In joint work with Hamkins, Klausner, Verner, and Williams in 2019, we studied the order-theoretic properties of the generic multiverse and, among other results, gave a characterization of which partial orders embed nicely into the multiverse. I will present our results in the simplest case of Cohen forcing, as well as existing generalizations to wide forcing, and some new results on non-Cohen ccc forcings.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 19 May, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Vera Fischer, University of Vienna
Title: tba
Abstract: tba
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

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Third European Set Theory Colloquium, today at 17:00-19:00 CEST

This is a reminder for the third European Set Theory Colloquium that will take place online at 17:00-19:00 CEST today. Please see the link for details.

Correction: 17:00 CEST = European summer time = Vienna local time is correct, not CET = Winter time.

Third European Set Theory Colloquium, this Thursday 17:00-19:00

This is a reminder for the third European Set Theory Colloquium that will take place online at 17:00-19:00 CEST on Thursday, 11 May 2023.

Please see the above link for details.

Online activities 1 – 7 May

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Baltic Set Theory Seminar
Time: Tuesday, 2 May, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
2. Paul Larson, A course on AD^+
Information: Please see the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 3 May, 13:00-15:00 Israel Time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

Leeds Models and Sets Seminar
Time: Wednesday, 3 May, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Vahagn Aslanyan, University of Leeds
Title: Combining Manin-Mumford and weak Zilber-Pink
Abstract: I will introduce some classical notions and problems in Diophantine geometry, including the Manin-Mumford and Zilber-Pink conjectures, and explain how model-theoretic tools are used to approach them. I will then talk about one of my recent theorems establishing a new partial result towards Zilber-Pink by combining Manin-Mumford and a weak version of Zilber-Pink (both are theorems). I am going to start with very basic things, give quite a few examples and define/explain all concepts that I am going to use, so I hope that most of the talk will be accessible to a wide range of people including those who have not heard about Diophantine geometry before.
Information: Please see the seminar webpage.

Caltech Logic Seminar
Time: Wednesday, 3 May, 12:00am-13:00pm Pacific time (21:00-22:00 CEST)
Speaker: Jan Grebík, University of Warwick
Title: Measurable Vizing’s theorem
Abstract: Vizing’s theorem asserts that every graph of degree bounded by Δ<+∞ admits a proper edge coloring with (Δ+1) colors. I will discuss versions of this theorem in the context of measurable graph combinatorics. I will mainly focus on the case when the graph in question is defined on a standard probability space (X,μ). In this situation, a combination of an augmenting chain technique developed earlier with Oleg Pikhurko (that was applied for graphings) together with a new result about quasi-invariant measures allows to deduce a full analogue of Vizing’s theorem.
Information: Please see the seminar webpage.

Renyi Institute Set Theory Seminar
Time: Thursday, 4 May, 10:30 – 12:00 CEST
Speaker: Lajos Soukup, Renyi Institute
Title: Minimal Vertex Covers in Infinite Hypergraphs
Abstract: A     “vertex cover” of a hypergraph is a  set of vertices which intersects each hyperedge. A hypergraph   possesses   “property C(k,ρ)”     iff  |⋂E′|<ρ for each k element set E′ of hyperedges. Komjáth proved that every uniform hypergraph possessing property C(2,r) for some   r∈ω has a minimal vertex cover. We could relax the assumption of uniformity to an assumption that the set of cardinalities of the hyperedges is a “small” set of infinite cardinals, e.g. it is countable, or it does not contain uncountably many limit cardinals. Komjáth also proved that GCH does not decide the following statement: “If a hypergraph  G possessing property C(2,ω)  is μ-uniform  for some μ≥ω1,  then G has a minimal vertex cover.
Using Shelah’s Revised GCH theorem,  we could show that if we strengthen the assumption μ≥ω1 to μ≥bethω, then we can prove the statement in ZFC! We also show that if all the  hyperedges of a hypergraph are  countably infinite,  then  instead of C(2,r) the assumption C(k,r) (for some  k∈ω) is enough to guarantee the existence of a minimal vertex cover. If every hyperedge has  cardinality  ω1, then we can only prove that  C(3,r)  is enough.
Information: Please see the seminar webpage. This talk will be given in hybrid format.

Vienna Research Seminar in Set Theory
Time: Tuesday, 4 May, 11:30-13:00 CEST
Speaker: L. Zdomskyy, TU Wien
Title: Cardinalities of sets of reals satisfying combinatorial covering properties
Abstract: We shall discuss which cardinalities sets of reals satisfying Menger and Hurewicz covering properties may have in some standard models of ZFC. Most of the results may be thought of as consistent instances of the Perfect Set Property, since they state that in some models, a set of reals satisfying certain covering properties either contains a copy of the Cantor set, or has small size. In particular, we plan to outline the proof of the fact that in the Sacks model every Menger totally imperfect set of reals has size at most ω1.
This is a joint work with V. Haberl and P. Szewczak.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 4 May, 15:00 – 15:45 CEST
Speaker: H. Mildenberger, University of Freiburg
Title: Destroying Guessing Principles
Abstract: An Ostaszewski club sequence is a weakening of Jensen’s diamond. In contrast to the diamond, the club does not imply the continuum hypothesis. Numerous questions about the club stay open, and we know only few models in which there is just a club sequence but no diamond sequence. In recent joint work with Shelah we found that a winning strategy for the completeness player in a bounding game on a forcing order does not suffice to establish the club in the extension.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 5 May, 16.00-17.00 CEST
Speaker: D. Sinapova, Rutgers University
Title: Mutual stationarity and the failure of SCH
Abstract: Mutual stationarity is a compactness type property for singular cardinals. Roughly, it asserts that given a singular cardinal κ, stationary subsets of regular cardinals with limit κ have a “simultaneous witness” for their stationarity. This principle was first defined by Foreman and Magidor in 2001, who showed that it holds for every sequence of stationary sets of cofinality ω. They also showed that their ZFC result does not generalize to higher cofinality. Whether the principle can consistently hold for higher cofinalities remained open, until a few years ago Ben Neria showed that from large cardinals mutual stationarity at ⟨ℵn∣n<ω⟩ can be forced for any fixed cofinality.
We show that we can obtain mutual stationarity at ⟨ℵn∣n<ω⟩ for any fixed cofinality together with the failure of SCH at ℵω. This is joint work with Will Adkisson.
Information: The event will stream on the Webex platform. Please write to  luca.mottoros [at] unito.it  for the link to the event.

CUNY Set Theory Seminar
Time: Friday, 5 May, 10:00am New York time (16:00 CEST)
Speaker: Joel David Hamkins, Notre Dame University
Title: Realizing Frege’s Basic Law V, provably in ZFC
Abstract: The standard set-theoretic distinction between sets and classes instantiates in important respects the Fregean distinction between objects and concepts, for in set theory we commonly take the universe of sets as a realm of objects to be considered under the guise of diverse concepts, the definable classes, each serving as a predicate on that domain of individuals. Although it is commonly held that in a very general manner, there can be no association of classes with objects in a way that fulfills Frege’s Basic Law V, nevertheless, in the ZF framework, it turns out that we can provide a completely deflationary account of this and other Fregean abstraction principles. Namely, there is a mapping of classes to objects, definable in set theory in senses I shall explain (hence deflationary), associating every first-order parametrically definable class F with a set object εF, in such a way that Basic Law V is fulfilled:
εF=εG↔∀x(Fx↔Gx). Russell’s elementary refutation of the general comprehension axiom, therefore, is improperly described as a refutation of Basic Law V itself, but rather refutes Basic Law V only when augmented with powerful class comprehension principles going strictly beyond ZF. The main result leads also to a proof of Tarski’s theorem on the nondefinability of truth as a corollary to Russell’s argument. A central goal of the project is to highlight the issue of definability and deflationism for the extension assignment problem at the core of Fregean abstraction.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 5 May, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Jeffrey Bergfalk, University of Barcelona
Title: Applications of nontrivial coherence
Abstract: This talk will survey some applications of infinitary combinatorics to superficially unrelated questions arising in the study of condensed mathematics, strong homology, and the derived limit functors, showing in the process that they all, combinatorially speaking, drink from the same well. At least as interesting as our ZFC answers to each of these questions are the further questions they open onto; we aim to survey these as well. This work is joint with Chris Lambie-Hanson, and carries a third aim of connecting with some of the material of his seminar talk of the preceding week; no dependency between the two talks, however, is intended.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 5 May, 2:00-3:30pm New York time (20:00-21:30 CEST)
Speaker: Karen Lange, Wellesley College
Title: Classification via effective lists
Abstract: ‘Classifying’ a natural collection of structures is a common goal in mathematics. Providing a classification can mean different things, e.g., identifying a set of invariants that settle the isomorphism problem or creating a list of all structures of a given kind without repetition of isomorphism type. Here we discuss recent work on classifications of the latter kind from the perspective of computable structure theory. We’ll consider natural classes of computable structures such as vector spaces, equivalence relations, algebraic fields, and trees to better understand the nuances of classification via effective lists and its relationship to other forms of classification in this setting.
Information: The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.

Third European Set Theory Colloquium, 11 May

The third European Set Theory Colloquium will take place online at 17:00-19:00 CEST on Thursday, 11 May 2023. The panelists are:

• Alan Dow, University of North Carolina at Charlotte
• Heike Mildenberger, University of Freiburg
• Slawek Solecki, Cornell University
• Matteo Viale, University of Torino

The zoom information for 11 May is:

Topic: EST Colloquium
Link: https://univienna.zoom.us/j/61733153940?pwd=Wm5sNjczVTlUWVA3Vy9pZlZreFlDQT09
Meeting ID: 617 3315 3940
Passcode: 582081

The EST colloquia take place online around four times per year. For each installment, four experts are invited to describe the general area they represent, explain where the area is heading and discuss how it relates to other areas of set theory and mathematics.

Sixth workshop on generalised Baire spaces, Vienna

The sixth version of the workshop on generalised Baire spaces will take place on July 26-28th at the Technical University of Vienna, some of the confirmed speakers are:

Omer Ben-Neria, The Hebrew University in Jerusalem.
Vera Fischer, University of Vienna.
Chris Lambie-Hanson, Czech Academy of Sciences.
Philipp Lücke, University of Barcelona.
Miguel Moreno, University of Vienna.
Dorottya Sziráki, Budapest.
Lyubomyr Zdomskyy, Technical University of Vienna.

If you would like to participate and/or contribute with a talk, contact me at dcmontoyaa@gmail.com. The workshop has a small registration fee of 50 Euros. Also, there is a preliminary website in the following link:

https://sites.google.com/view/gbs23/startseite

Please feel free to forward this information to anyone, who may be interested and do not hesitate to contact me in case you have any questions or comments.

Best wishes and looking forward to seeing you in Vienna,

Diana Carolina Montoya

Online activities 24 – 30 April

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Vienna Research Seminar in Set Theory
Time: Tuesday, 25 April, 15:00-16:30 CEST
Speaker: T. Żuchowski, Wrocław University
Title: Nonseparable growth of ω supporting a strictly positive measure
Abstract: During the talk I will present a construction in ZFC of a compactification of ω such that its remainder is not separable and carries a strictly positive measure, i.e. measure positive on nonempty open subsets. The measure is defined using the asymptotic density of subsets of ω. The remainder is a Stone space of some Boolean subalgebra of Borel subsets of the Cantor space containing all clopen sets, constructed with an aid of an uncountable almost disjoint family of subsets of ω. This is a joint work with Piotr Borodulin-Nadzieja.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 25 April, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 26 April, 13:00-15:00 Israel Time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

Renyi Institute Set Theory Seminar
Time: Thursday, 26 April, 10:30 – 12:00 CEST
Speaker: Lajos Soukup, Renyi Institute
Title: Elusive graph properties
Abstract: A graph property is said to be  elusive (or evasive) if every algorithm testing this property by asking questions of the form  “ is there an edge between vertices x and y?” requires, in the worst case, to ask about all pairs of vertices. The unsettled Aanderaa-Karp-Rosenberg conjecture is that every non-trivial monotone graph property is elusive for any finite vertex set.
We show that the situation is completely different for infinite vertex sets: the monotone graph properties  “every vertex has degree at least n” and  “every connected component has size at least m”, where n ≥ 1 and m ≥ 2 are natural numbers, are not elusive for infinite vertex sets, but the monotone graph property ” the graph contains a cycle” is elusive for arbitrary vertex set.
On the other hand, we also prove that every algorithm testing some natural monotone graph properties  should check “lots of edges”, e.g, all the edges of an infnite complete subgraph.
Information: This talk will be given in hybrid format. Please see the seminar website.

CUNY Set Theory Seminar
Time: Friday, 28 April, 12:15pm New York time (18:15 CEST)
Speaker: Will Boney, Texas State University
Title: tba
Abstract: tba
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 28 April, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Chris Lambie-Hanson
Title: Whitehead’s problem and condensed mathematics
Abstract: Whitehead’s problem, which asks whether every Whitehead abelian group is a free abelian group, was a prominent open question in group theory in the mid-20th century. In 1974, Shelah proved that the problem is independent of ZFC, which was a surprising development and provided one of the first instances of a major problem coming from outside logic and set theory to be proven independent of ZFC. In recent years, Clausen and Scholze have introduced the category of condensed abelian groups, which can be seen as an enrichment of the category of topological abelian groups with nicer algebraic properties. Through some deep structural analysis of this category, they showed that, when appropriately interpreted, Whitehead’s problem is not independent in the category of condensed abelian groups: it is provable in ZFC that every abelian group that is Whitehead in the condensed category must be free. In this talk, we sketch a new, more concrete proof of Clausen and Scholze’s result, in the process highlighting some connections between condensed mathematics and the theory of forcing. This is joint work with Jeffrey Bergfalk and Jan Šaroch.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

Online activities 17-23 April

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Baltic Set Theory Seminar
Time: Tuesday, 18 April, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 18 April, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)  
Speaker: Martin Zeman, University of California, Irvine
Title: Distributivity of iterated club shooting and fine structural models, part 3
Abstract: Iterative adding closed unbounded sets through stationary sets found quite a few applications in set theory. One natural way to do this is adding club sets using posets consisting of initial segments of the desired clubs. In such situations, one important property of such iterations is sufficient distributivity. In fact, establishing distributivity is often the main part of arguments that involve iterated club shooting.
There are two possible situations where one iteratively adds clubs. First, for a fixed cardinal $\kappa$, one iteratively adds club subsets of $\kappa^+$. This kind of construction proved to have many applications. Second, one may start with a cardinal $\delta$ and iteratively add club subsets of cardinals $\kappa^+$ where $\kappa$ ranges over some set above $\delta$. Surprisingly, this kind of construction has not been much studied. In this talk we will focus on this situation.
In order to add a club subset of some stationary set $S$ the set $S$ must be large in a certain sense; such sets are called fat. It is known that, consistently, iterative adding club subsets of fat stationary sets of $\omega_n$ on a tail-end of $n\in\omega$ followed by forming an inverse limit at the end may collapse $\aleph_n$ to $\omega$. A strong form of fatness is the property of being the complement of a non-reflecting stationary set. One can prove, using a fairly standard argument, that if the iteration described above uses complements of non-reflecting stationary sets instead of just fat sets, then such an iteration is $(\omega_{n+1},\infty)$-distributive where $\omega_n$ is the first active step in the iteration. One can also prove in ZFC that the analogous  amount of distributivity holds of longer iterations, where the first active step is at $\delta$ and inverse limits are used at singular steps, as long as the singular steps are of cofinality $<\delta$. Passing through singular steps of cofinality $\ge\delta$ seems to be difficult, and we only know how to do this over a fine structural model where the non-reflecting stationary sets are carefully chosen. Even in such a seemingly special case, the method does have applications.
This is a part of a joint work of Foreman-Magidor-Zeman on games with filters.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

Caltech Logic Seminar
Time: Tuesday, 18 April, 11:00am-12:00pm Pacific time (20:00-21:00 CEST)
Speaker: Anton Bernshteyn, Georgia Institute of Technology
Title: The Local Lemma in descriptive combinatorics: survey and recent developments
Abstract: The Lovász Local Lemma is a classical tool in probabilistic combinatorics with numerous and diverse applications. In this talk, I will survey what is known about the behavior of the Local Lemma in the Borel and measurable context, including some very recent progress, and state several open problems. Part of this talk is based on joint work with Felix Weilacher.
Information: Please see the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 19 April, 13:00-15:00 Israel Time (12:00-14:00 CEST)
Speaker: Yair Hayut
Title: Sealing Kurepa trees, continued
Abstract: In this talk, I’m going to describe Itamar Giron’s master thesis. Most of the results in this talk are due to him. 
The main question of the thesis was whether there is a forcing notion that makes an arbitrary Kurepa tree into a non-distributive one, and how far can one go in this direction (can we get sealed Kurepa trees?).
We will start with the classical construction of a Kurepa tree in L (by Solovay). We will show that this tree is distributive in L. We will review the known constructions due to Poor and Shelah (generalized by Muller and me), of sealed Kurepa trees in L (can be generalized to canonical inner models).  
Then, we will also find a forcing extension in which for every Kurepa tree, one can add a branch without collapsing cardinals.  This means that even though it is easy to find non-distributive Kurepa trees, it is far less trivial to get from combinatorial assertions (such as diamond*), a sealed Kurepa tree. 
Finally, I will talk about the forcing notion that “specializes” a Kurepa tree over an arbitrary model of ZFC. This is Giron’s main result, which requires the most sophisticated tools. 
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

Vienna Research Seminar in Set Theory
Time: Thursday, 20 April, 11:30-13:00 CEST
Speaker: L. Zdomskyy, TU Wien
Title: Menger spaces everywhere
Abstract: Combinatorial covering properties, which arose from the study of classical special sets of reals, appear in many contexts in topology and set theory. In this talk we shall discuss some applications of the Menger property and certain stronger versions thereof. It is planned to be a gentle introduction to the next talk on April 27.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 20 April, 15:00 – 15:45 CEST
Speaker: Z. Vidnyánszky, Eötvös Loránd University
Title: Homomorphism problems in the infinite context
Abstract: The CSP dichotomy of Bulatov and Zhuk is a celebrated theorem of computer science: it states that given a finite structure H, deciding whether a structure G admits a homomorphism to G is either easy (in P) or hard (NP-complete). We will discuss two infinitary versions of this theorem. First, following Thornton, in the Borel con ext. Here a striking difference from the finite world emerges: we will show that solving linear equations over a finite field is already hard (Σ12-complete). Second, assuming only ZF, we will consider the relationship of the H-compactness properties, that is, the statement that for every G if every finite substructure of G admits a homomorphism to H then so is G. Here we show that there exists a model M of ZF, such that M⊨H-compactness iff the H-homomorphism problem is easy.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 21 April, 16.00-17.00 CEST
Speaker: M. Elekes, Rényi Institute and Eötvös Loránd University
Title: tba
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.

CUNY Set Theory Seminar
Time: Friday, 21 April, 12:15pm New York time (18:15 CEST)
Speaker: Mohammad Golshani, Institute for Research in Fundamental Sciences
Title: The proper forcing axiom for ℵ1-sized posets and the continuum
Abstract: We discuss Shelah’s memory iteration technique and use it to show that the PFA for posets of size ℵ1 is consistent with large continuum. This is joint work with David Aspero.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 21 April, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Cesar Corral, Universidad Nacional Autónoma de México
Title: tba
Abstract: tba
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 21 April, 2:00 – 3:30 New York time (20:00-21:30 CEST)
Speaker: James Hanson, University of Maryland
Title: How bad could it be? The semilattice of definable sets in continuous logic
Abstract: Continuous first-order logic is a generalization of discrete first-order logic suited for studying structures with natural underlying metrics, such as operator algebras and R-trees. While many things from discrete model theory generalize directly to continuous model theory, there are also new subtleties, such as the correct notion of ‘definability’ for subsets of a structure. Definable sets are conventionally taken to be those that admit relative quantification in an appropriate sense. An easy argument then establishes that the union of definable sets is definable, but in general the intersection of definable sets may fail to be. This raises the question of which semilattices arise as the partial order of definable sets in a continuous theory.
After giving an overview of the basic properties of definable sets in continuous logic, we will give a largely visual proof that any finite semilattice (and therefore any finite lattice) is the partial order of definable sets in some superstable continuous first-order theory. We will then discuss a partial extension of this to certain infinite semilattices.
Information: The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.

University of Leeds Löb Lecture — Justin Moore 13-14 April (hybrid)

The University of Leeds Logic Group is pleased to announce that the 2023 Löb Lecture will be given by Prof. Justin Moore (Cornell University).

The Löb Lecture and related talks will take place on 13-14 April.  The talks will be broadcast via Zoom.  To register for online participation, please send an email to Paul Shafer at <P.E.Shafer@leeds.ac.uk>.  Please include:

* Subject line: LÖB 2023 REGISTRATION
* Your name
* Your institution

Please see below for the schedule and abstracts.

The Löb Lecture is held quadrennially in memory of Professor Martin H. Löb (1921-2006), the founder of the internationally-known Mathematical Logic Group within the University of Leeds School of Mathematics.


Löb Lecture and related talks
13-14 April 2023
<https://logic.leeds.ac.uk/lob-lecture/>

Logic Seminar
Thursday, 13 April 2pm UK time
Speaker:  Justin Moore (Cornell University)
Title:  Ordinal arithmetic and subgroups of Thompson’s group

Introductory Lecture
Friday, 14 April 2pm UK time
Speaker: Asaf Karagila (University of Leeds)
Title:  What, why, and how are Forcing Axioms?

Löb Lecture
Friday, 14 April 4pm UK time
Speaker:  Justin Moore (Cornell University)
Title:  What makes the continuum aleph_2


==
Logic Seminar
Justin Moore (Cornell University)
Ordinal arithmetic and subgroups of Thompson’s group

The class of finitely generated groups embeddable into Richard Thompson’s group F is both restrictive and rich at the same time.  We show that there is a family of groups within this class which is pre-well-ordered in type epsilon_0 by the embeddability relation.  Moreover, the operations of addition and multiplication on the ordinals translate into natural group-theoretic operations—direct sum and a type of permutational wreath product.  This talk will give a description of this correspondence.  This is joint work with Collin Bleak and Matt Brin.
==

==
Introductory Lecture
Asaf Karagila (University of Leeds)
What, why, and how are Forcing Axioms?

Forcing axioms are set-theoretic axioms which postulate the existence of “somewhat generic objects” in the universe.  The goal of this talk is to give a fairly accessible explanation of this sentence, to understand some of the consequences of forcing axioms, and in what sense some forcing axioms are stronger than others.
==

==
Löb Lecture
Justin Moore (Cornell University)
What makes the continuum aleph_2

While historically the question has been whether the Continuum Hypothesis is true or false, determining the relationship between the continuum and aleph_2 (the second uncountable cardinal) is arguably a much deeper and more interesting mathematical problem.  I will lay out a philosophical and mathematical argument for why aleph_2 is the right value for the continuum.
==


Best wishes,
Paul Shafer, on behalf of the Leeds Logic Group

Online activities 10-16 April

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Baltic Set Theory Seminar
Time: Tuesday, 11 April, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 11 April, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)  
Speaker: Martin Zeman, University of California, Irvine
Title: Distributivity of iterated club shooting and fine structural models, part 2
Abstract: Iterative adding closed unbounded sets through stationary sets found quite a few applications in set theory. One natural way to do this is adding club sets using posets consisting of initial segments of the desired clubs. In such situations, one important property of such iterations is sufficient amount of distributivity. In fact, establishing distributivity is often the main part of arguments that involve iterated club shooting.
There are two possible situations where one iteratively adds clubs. First, for a fixed cardinal $\kappa$, one iteratively adds club subsets of $\kappa^+$. This kind of construction proved to have many applications. Second, one may start with a cardinal $\delta$ and iteratively add club subsets of cardinals $\kappa^+$ where $\kappa$ ranges ofer some set above $\delta$. Surprisingly, this kind of construction has not been much studied. In this talk we will focus on this situation.
In order to add a club subset of some stationary set $S$ the set $S$ must be large in certain sense; such sets are called fat. It is known that, consistently, iterative adding club subsets of fat stationary sets of $\omega_n$ on a tail-end of $n\in\omega$ followed by forming an inverse limit at the end may collapse $\aleph_n$ to $\omega$. A strong form of fatness is the property of being the complement of a non-reflecting stationary set. One can prove, using a fairly standard argument, that if the iteration described above uses complements of non-reflecting stationary sets instead of just fat sets, then such an iteration is $(\omega_{n+1},\infty)$-distributive where $\omega_n$ is the first active step in the iteration. One can also prove in ZFC that the analogous  amount of distributivity holds of longer iterations, where the first active step is at $\delta$ and inverse limits are used at singular steps, as long as the singular steps are of cofinality $<\delta$. Passing through singular steps of cofinality $\ge\delta$ seems to be difficult, and we only know how to do this over a fine structural model where the non-reflecting stationary sets are carefully chosen. Even in such a seemingly special case, the method does have applications.
This is a part of a joint work of Foreman-Magidor-Zeman on games with filters.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

Caltech Logic Seminar
Time: Tuesday, 11 April, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: William Chan, University of North Texas
Title: Cardinalities Below the Power Set of the First Uncountable Cardinals
Abstract: This talk will survey the known structure of cardinalities below the power set of the first uncountable cardinal under various determinacy assumptions. Regularity and cofinality of cardinalities will be formulated. Combinatorial aspects of cardinalities such as primeness and Jónssonness may also be discussed. Portions of this talk includes joint work with Jackson and Trang.
Information: Please see the seminar webpage.

CMU Logic Seminar
Time: Tuesday, 11 April, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)  
Speaker: Samuele Giraudo, Université du Québec à Montréal
Title: Some enumerative and order-theoretic properties in combinatory logic
Abstract: In the field of combinatory logic, every term specifies a multigraph consisting of the set of terms that can be reached from it. By adopting an algebraic and combinatorial approach, we investigate various properties of these multigraphs. Specifically, we address enumerative questions, such as whether the multigraph of a term is finite, and if so, how many elements it contains. We also explore order-theoretic questions, such as whether the reflexive and transitive closure of the rewrite relation constitutes a partially ordered set or even a lattice. In this work-in-progress, we present our initial findings in this area.
Information: See the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, 14 April, 12:15pm New York time (18:15 CET)
Speaker: Gabriel Goldberg, University of California, Berkeley
Title: Cardinal preserving embeddings and strongly compact cardinals
Abstract: Kunen’s theorem that there is no elementary embedding from V to V seems to set an upper bound on the hierarchy of large cardinal axioms. Challenging this, Caicedo asked what happens when V is replaced with an inner model M that is very close to V in the sense that M correctly computes the class of cardinals. Assuming the existence of strongly compact cardinals, we show that there is no elementary embedding from such an inner model M into V or from V into M. The former result (M into V) is joint work with Sebastiano Thei. Without strong compactness assumptions, both questions remain open, but we’ll discuss some partial results.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 14 April, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: David Fernández-Bretón, Instituto Politécnico Nacional
Title: Hindman’s theorem in the hierarchy of choice principles
Abstract: We will explain how to state Hindman’s theorem in a way that provides a statement provable from ZFC but not from ZF alone. This gives us a way of considering Hindman’s theorem as a weak version of the Axiom of Choice; we will discuss where this statement fits within the hierarchy of weak choice principles, and provide a few independence proofs, involving this principle, within ZF —this will require us to outline the Fraenkel-Mostowski method for providing independence proofs in ZFA.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.