PhD Research Position in Münster

The Institute of Mathematical Logic and Foundational Research at the
University of Münster, Germany, offers a

PhD Research Position in Set Theory
Wissenschaftliche/r Mitarbeiter/in
(salary level TV-L E13, 75%)

The duration of the position is 3 years. The expected starting date is
1 November 2020. Currently, the regular working time for 75%
employment is 29 hours and 52 minutes per week. The position carries
no teaching duties.

The position is funded by the Deutsche Forschungsgemeinschaft (DFG)
and is situated within the DFG Research Project “Long extenders,
Varsovian models, Combinatorics”, led by Junior Professor Farmer
Schlutzenberg. The successful applicant will collaborate on this
project which is directed at various questions in set theory, with a
focus on inner models and large cardinals. Applicants working in these
and related areas are welcome.

The University of Münster is an equal opportunity employer and is
committed to increasing the proportion of women academics.
Consequently, we actively encourage applications by women.
Female candidates with equivalent qualifications and academic
achievements will be preferentially considered within the framework of
the legal possibilities.

The University of Münster is committed to employing more staff with
disabilities. Candidates with recognised severe disabilities who have
equivalent qualifications are given preference in hiring decisions.

Applications should include a cover letter, CV, diplomas of your
academic degrees (bachelor, master’s, or diploma) and transcripts of
the courses taken, including marks/grades. Please arrange for two
letters of recommendation.

The deadline for applications, including letters of recommendation, is
1 August 2020.

Applications, letters of recommendation (or any inquiries) should be
sent via e-mail to:

JProf Dr Farmer Schlutzenberg at schlutze@uni-muenster.de .

Online activities: week 29 June – 5 July 2020

June 29

Bristol Logic and Set Theory Seminar (recurring lecture series)
Time:
 Wednesday, July 1, 13:30-15:00 UK time (14:30-16:00 CEST)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines X
Abstract: This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: zoom via https://zoom.us/j/96803195711 (open 30 minutes before).

CUNY Logic Seminar (MOPA)
Time: Wednesday, July 1, 14:00 New York time (20:00 CEST)
Speaker: Zachiri McKenzie
Title: Initial self-embeddings of models of set theory: Part II
Abstract: In the 1973 paper ‘Countable models of set theory’, H. Friedman’s investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of ‘initial segment’: transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman’s self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms ‘initial self-embeddings’. I will outline a proof of a refinement of H. Friedman’s Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman’s Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.​
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Set Theory Seminar
Time: Friday, July 3, 14:00 New York time (20:00 CEST)
Speaker: Vera Fischer, University of Vienna
Title: More ZFC inequalities between cardinal invariants
Abstract: We will discuss some recent ZFC results concerning the generalized Baire spaces, and more specifically the generalized bounding number, relatives of the generalized almost disjointness number, as well as generalized reaping and domination.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online activities: week 22-28 June 2020

June 23

Münster Set Theory Seminar
Time: Tuesday, June 23, 4:15pm CEST
Speaker: Farmer Schlutzenberg
Title: Remarks on rank-into-rank embeddings part III
Abstract: Recall that Woodin’s large cardinal axiom I0 gives an ordinal λ and an elementary embedding j:L(V_{λ+1})→L(V_{λ+1}) with critical point <λ. Using methods due to Woodin, we show that if ZFC+I0 is consistent then so is ZF+DC(λ)+ there is an ordinal λ and an elementary j:V_{λ+2}→V_{λ+2}”. (A version with the added assumption that V_{λ+1}^sharp exists is due to the author, and Goldberg observed that the appeal to V_{λ+1}^sharp could actually be replaced by some further calculations of Woodin’s.)
Reference: https://arxiv.org/abs/2006.01077, “On the consistency of  ZF with an elementary embedding from V_{λ+2} into V_{λ+2}”.
Information: contact rds@wwu.de ahead of time in order to participate.

June 24

Bar-Ilan University and Hebrew University Set Theory Seminar
Time: Wednesday, June 24, 11:00-13:00 Israel time (10:00-13:00 CEST)
Speaker: Istvan Juhasz
Title: On the free subset number of a topological space and their G_\delta modification
Abstract: pdf available on seminar website.
Information: Contact Assaf Rinot for the zoom id.

Bristol Logic and Set Theory Seminar (recurring lecture series)
Time:
 Wednesday, June 24, 13:30-15:00 UK time (14:30-16:00 CEST)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines IX
Abstract:
This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: zoom via https://zoom.us/j/96803195711

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, June 24, 16:00-17:15 CEST
Speaker: Ludovic Patey, University of Lyon
Title: The computability-theoretic aspects of Milliken’s tree theorem and
applications
Abstract: Milliken’s tree theorem states that for every countable, finitely
branching tree T with no leaves, and every finite coloring f of the
strong subtrees of height n, there is an infinite strong subtree over
which the strong subtrees of height n are monochromatic. This theorem
has several applications, among which Devlin’s theorem about finite
coloring of the rationals, and a theorem about the Rado graph. In this
talk, we give a survey of the computability-theoretic aspects of these
statements seen as mathematical problems, in terms of instances and
solutions. Our main motivation is reverse mathematics. This is a joint
work with Paul-Elliot Anglès d’Auriac, Peter Cholak and Damir Dzhafarov.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, June 24, 15:00-16:30 UK time (16:00-17:30 CEST)
Speaker: Alessandro Andretta, University of Torino
Title: Generalised iteration trees
Abstract:
A theorem of Gaifman states that any internal linear iteration whose length belongs to the model it is applied to has a well-founded direct limit.We have isolated a notion of “generalized iteration trees” for which a similar result is possible, at least if the length of the tree is $\omega$. These iterations are more general than the objects introduced by Martin and Steel over three decades ago in that the extender $E_n$ used to construct $M_{n+1}$ need not to belong to the last model $M_n$. In other words $E_n \in M_{d(n+1)}$, with $d(n+1) \leq n$. We isolate a simple property of the function $d$ characterizing continuous ill-foundedness of generalized iteration trees.Any  generalized iteration trees satisfying this property is not continuously ill-founded. Conversely, any tree order with a $d$ function failing such property can be realized as a continuously ill-founded iteration tree on V.
This is joint work with John Steel.
Information: zoom via https://zoom.us/j/96803195711

CUNY Logic Seminar (MOPA)
Time: Wednesday, June 24, 14:00 New York time (20:00 CEST)
Speaker: Bartosz Wcisło, Polish Academy of Sciences
Title: Tarski boundary III
Abstract: Truth theories investigate the notion of truth using axiomatic methods. To a fixed base theory (typically Peano Arithmetic PA) we add a unary predicate T(x) with the intended interpretation ‘x is a (code of a) true sentence’. Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour. One of the aspects which we are trying to understand is which truth-theoretic principles make the added truth predicate ‘strong’ in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this demarcating line between conservative and non-conservative truth theories ‘the Tarski boundary’. Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PA or exactly equivalent to the principle of global reflection over A. It says that sentences provable in PA are true in the sense of the predicate T. This in turn is equivalent to Δ_0-induction for the compositional truth predicate which turns out to be a surprisingly robust theory. The equivalences between nonconservative truth theories are typically proved by relatively direct ad hoc arguments. However, certain patterns seem common to these proofs. The first one is construction of various arithmetical partial truth predicates which provably in a given theory have better properties than the original truth predicate. The second one is deriving induction for these truth predicates from internal induction, a principle which says that for any arithmetical formula, the set of those elements for which that formula is satisfied under the truth predicate satisfies the usual induction axioms. As an example of this phenomenon, we will present two proofs. First, we will show that global reflection principle is equivalent to local induction. Global reflection expresses that any sentence provable in PA is true. Local induction says that any predicate obtained by restricting truth predicate to sentences of a fixed syntactic complexity satisfies full induction. This is an observation due to Mateusz Łełyk and the author of this presentation. The second example is a result by Ali Enayat who showed that CT_0, a theory compositional truth with Δ_0-induction, is arithmetically equivalent to the theory of compositional truth together with internal induction and disjunctive correctness.This talk is intended as a continuation of ‘Tarski boundary II’ presentation at the same seminar. However, we will try to avoid excessive assumptions on familiarity with the previous part.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

June 25

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, June 25, 16:00 CEST
Speaker: Victoria Gitman, CUNY
Title: Class forcing in its rightful setting
Abstract: The use of class forcing in set theoretic constructions goes back to the proof Easton’s Theorem that GCH can fail at all regular cardinals. Class forcing extensions are ubiquitous in modern set theory, particularly in the emerging field of set-theoretic geology. Yet, besides the pioneering work by Friedman and Stanley concerning pretame and tame class forcing, the general theory of class forcing has not really been developed until recently. A revival of interest in second-order set theory has set the stage for understanding the properties of class forcing in its natural setting. Class forcing makes a fundamental use of class objects, which in the first-order setting can only be studied in the meta-theory. Not surprisingly it has turned out that properties of class forcing notions are fundamentally determined by which other classes exist around them. In this talk, I will survey recent results (of myself, Antos, Friedman, Hamkins, Holy, Krapf, Schlicht, Williams and others) regarding the general theory of class forcing, the effects of the second-order set theoretic background on the behavior of class forcing notions and the numerous ways in which familiar properties of set forcing can fail for class forcing even in strong second-order set theories.
Information: Talk via zoom.

June 26

CUNY Set Theory Seminar
Time: Friday, June 26, 2pm New York time (8pm CEST)
Speaker: Joel David Hamkins, Oxford
Title: Categorical cardinals
Abstract: Zermelo famously characterized the models of second-order Zermelo-Fraenkel set theory ZFC_2 in his 1930 quasi-categoricity result asserting that the models of ZFC_2 are precisely those isomorphic to a rank-initial segment V_κ of the cumulative set-theoretic universe V cut off at an inaccessible cardinal κ. I shall discuss the extent to which Zermelo’s quasi-categoricity analysis can rise fully to the level of categoricity, in light of the observation that many of the V_κ universes are categorically characterized by their sentences or theories. For example, if κ is the smallest inaccessible cardinal, then up to isomorphism V_κ is the unique model of ZFC_2 plus the sentence ‘there are no inaccessible cardinals.’ This cardinal κ is therefore an instance of what we call a first-order sententially categorical cardinal. Similarly, many of the other inaccessible universes satisfy categorical extensions of ZFC_2 by a sentence or theory, either in first or second order. I shall thus introduce and investigate the categorical cardinals, a new kind of large cardinal. This is joint work with Robin Solberg (Oxford).
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, June 26, 1.30pm Toronto time (7.30pm CEST)
Speaker: Will Brian (UNC Charlotte)
Title: Limited-information strategies in Banach-Mazur games.
Abstract: The Banach-Mazur game is an infinite-length game played on a topological space X, in which two players take turns choosing members of an infinite decreasing sequence of open sets, the first player trying to ensure that the intersection of this sequence is empty, and the second that it is not. A limited-information strategy for one of the players is a game plan that, on any given move, depends on only a small part of the game’s history. In this talk we will discuss Telgársky’s conjecture, which asserts roughly that there must be topological spaces where winning strategies for the Banach-Mazur game cannot be too limited, but must rely on large parts of the game’s history in a significant way. Recently, it was shown that this conjecture fails in models of set theory satisfying GCH + \Box. In such models it is always possible for one player to code all information concerning a game’s history into a small piece of it. We will discuss these so-called coding strategies, why assuming GCH + \Box makes them work so well, and what can go wrong in other models of set theory.
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Online activities: week 15th-22nd of June 2020

June 16

Udine graduate course
Time:
 Tuesday, June 16, 10:00-12:00 CEST
Speaker: Vincenzo Dimonte, University of Udine
Title: Generalized Descriptive Set Theory II, Lecture 4
Abstract: The objective of the course is to prove an analogue of Silver’s Theorem for the space $2^\lambda$, where $\lambda$ is an uncountable cardinal of cofinality $\omega$, using some large cardinal strength (the proof is still unpublished).
This result has been chosen as an example to show, more in general, how to generalize a deep classical theorem in this setting, which properties of singular cardinals are useful in that respect, and what are the main obstacles of the generalization. The proof will use some peculiarities of singular cardinal combinatorics and some large cardinal strength, and everything will be introduced in the first three lessons. 
The course is self-contained (despite the name), the only prerequisite is to know basic set theory (the theory of forcing, the most basic descriptive set theory, maybe inaccessible cardinals).
The following is a tentative schedule:Tuesday 10.00-12.00 CEST, Friday 10.00-12.00 CEST, from 5 June 2020, for 5 lessons.
Lesson 1: Measurable cardinals
Lesson 2: Prikry forcing, diagonal Prikry forcing
Lesson 3: Strong Prikry condition, “double” diagonal Prikry forcing
Lesson 4: generalized G_0 dichotomy
Lesson 5: generalized Silver Theorem
Information: Via Microsoft Teams, to participate contact vincenzo.dimonte@uniud.it.

Münster Set Theory Seminar
Time: Tuesday, June 16, 4:15pm CEST
Speaker: Farmer Schlutzenberg
Title: Remarks on rank-into-rank embeddings part II
Abstract: Recall that Woodin’s large cardinal axiom I0 gives an ordinal λ and an elementary embedding j:L(V_{λ+1})→L(V_{λ+1}) with critical point <λ. Using methods due to Woodin, we show that if ZFC+I0 is consistent then so is ZF+DC(λ)+ there is an ordinal λ and an elementary j:V_{λ+2}→V_{λ+2}”. (A version with the added assumption that V_{λ+1}^sharp exists is due to the author, and Goldberg observed that the appeal to V_{λ+1}^sharp could actually be replaced by some further calculations of Woodin’s.)
Reference: https://arxiv.org/abs/2006.01077, “On the consistency of  ZF with an elementary embedding from V_{λ+2} into V_{λ+2}”.
Information: contact rds@wwu.de ahead of time in order to participate.

June 17

Bar-Ilan University and Hebrew University Set Theory Seminar
Time: Wednesday, April 17, 11:00-13:00 Israel time (10:00-13:00 CEST)
Speaker: Mirna Dzamonja (University of East Anglia)
Title: Wide Aronszajn trees
Abstract: A wide Aronszajn tree is a tree is size and height omega_1 but with no uncountable branch. Such trees arise naturally in the study of model-theoretic notions on models of size aleph_1 as well as in generalised descriptive set theory. In their 1994 paper devoted to various aspects of such trees, Mekler and Väänänen studied the so called weak embeddings between such trees, which are simply defined as strict-order preserving functions. Their work raised the question if under MA there exists a universal wide Aronszajn tree under such embeddings. We present a negative solution to this question, obtained in a paper to appear, joint with Shelah. We also discuss various connected notions and the history of the problem. 
Information: Contact Assaf Rinot for the zoom id.

Bristol Logic and Set Theory Seminar (recurring lecture series)
Time:
 Wednesday, June 17, 13:30-15:00 UK time (14:30-16:00 CEST)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines VIII
Abstract:
This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: zoom via https://zoom.us/j/96803195711

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, June 17, 16:00-17:15 CEST
Speaker: Michał Skrzypczak – Université de Varsovie
Title: Measure theory and Monadic Second-order logic over infinite trees
Abstract: Monadic Second-order (MSO) logic is a well-studied formalism featuring many decision procedures and effective transformations. It is the fundamental logic considered in automata theory, equivalent to various other ways of defining sets of objects. In this talk, I will speak about the expressive power of MSO over infinite binary trees (i.e. free structures of two successors) – the theory from the famous Rabin’s decidability result.
The goal of the talk is to survey recent results about measure properties of MSO-definable sets of infinite trees. First, I will argue that these sets are indeed measurable (which is not obvious, as there exist non-Borel sets definable in MSO). Then I will move to the question of our ability to compute the measure of the set defined by a given formula. Although the general question is still open (and seems to be demanding), I will speak about decidability results for fragments of MSO, focusing on the so-called weak-MSO.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Oxford Set Theory Seminar
Time:
 Wednesday, June 17, 16:00-17:30 UK time (17:00-18:30 CEST)
Speaker: Corey Bacal Switzer, City University of New York
Title: Some Set Theory of Kaufmann Models
Abstract: A Kaufmann model is an ω1-like, recursively saturated, rather classless model of PA. Such models were shown to exist by Kaufmann under the assumption that ♢ holds, and in ZFC by Shelah via an absoluteness argument involving strong logics. They are important in the theory of models of arithmetic notably because they show that many classic results about countable, recursively saturated models of arithmetic cannot be extended to uncountable models. They are also a particularly interesting example of set theoretic incompactness at ω1, similar to an Aronszajn tree.
In this talk we’ll look at several set theoretic issues relating to this class of models motivated by the seemingly naïve question of whether or not such models can be killed by forcing without collapsing ω1. Surprisingly the answer to this question turns out to be independent: under MAℵ1 no ω1-preserving forcing can destroy Kaufmann-ness whereas under ♢ there is a Kaufmann model M and a Souslin tree S so that forcing with S adds a satisfaction class to M (thus killing rather classlessness). The techniques involved in these proofs also yield another surprising side of Kaufmann models: it is independent of ZFC whether the class of Kaufmann models can be axiomatized in the logic Lω1,ω(Q) where Q is the quantifier “there exists uncountably many”. This is the logic used in Shelah’s aforementioned result, hence the interest in this level of expressive power.
Information: For the Zoom access code, contact Samuel Adam-Day: me@samadamday.com.

CUNY Set Theory Seminar
Time: Wednesday, June 17, 14:00 New York time (20:00 CEST)
Speaker: Mateusz Łełyk, University of Warsaw
Title: Partial Reflection over Uniform Disquotational Truth
Abstract: In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form ∀x(ProvTh(ϕ(x˙))→ϕ(x)).
Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.
This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is ∀xT(ϕ(x˙))≡ϕ(x).
The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed Σn-complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0 (the theory of compositional truth with Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło’s talk). Beklemishev and Pakhomov leave the following open question: Is Σ1-reflection principle over the uniform disquotational scheme provable in CT0? The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in
CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of
Δ_0-reflection over the disquotational scheme.Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

June 18

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, June 18, 16:00 CEST
Speaker: Anush Tserunyan, University of Illinois at Urbana-Champaign
Title: Hyperfinite subequivalence relations of treed equivalence relations
Abstract: A large part of measured group theory studies structural properties of countable groups that hold “on average”. This is made precise by studying the orbit equivalence relations induced by free Borel actions of these groups on a standard probability space. In this vein, the amenable groups correspond to hyperfinite equivalence relations, and the free groups to the treeable ones. In joint work with R. Tucker-Drob, we give a detailed analysis of the structure of hyperfinite subequivalence relations of a treed equivalence relation on a standard probability space, deriving the analogues of structural properties of amenable subgroups (copies of ℤZ) of a free group. Most importantly, just like every such subgroup is contained in a unique maximal one, we show that even in the non-pmp setting, every hyperfinite subequivalence relation is contained in a unique maximal one.
Information: Talk via zoom.

June 19

Udine graduate course
Time:
 Friday, June 19, 10:00-12:00 CEST
Speaker: Vincenzo Dimonte, University of Udine
Title: Generalized Descriptive Set Theory II, Lecture 5
Abstract: The objective of the course is to prove an analogue of Silver’s Theorem for the space $2^\lambda$, where $\lambda$ is an uncountable cardinal of cofinality $\omega$, using some large cardinal strength (the proof is still unpublished).
This result has been chosen as an example to show, more in general, how to generalize a deep classical theorem in this setting, which properties of singular cardinals are useful in that respect, and what are the main obstacles of the generalization. The proof will use some peculiarities of singular cardinal combinatorics and some large cardinal strength, and everything will be introduced in the first three lessons. 
The course is self-contained (despite the name), the only prerequisite is to know basic set theory (the theory of forcing, the most basic descriptive set theory, maybe inaccessible cardinals).
The following is a tentative schedule:Tuesday 10.00-12.00 CEST, Friday 10.00-12.00 CEST, from 5 June 2020, for 5 lessons.
Lesson 1: Measurable cardinals
Lesson 2: Prikry forcing, diagonal Prikry forcing
Lesson 3: Strong Prikry condition, “double” diagonal Prikry forcing
Lesson 4: generalized G_0 dichotomy
Lesson 5: generalized Silver Theorem
Information: Via Microsoft Teams, to participate contact vincenzo.dimonte@uniud.it.

CUNY Set Theory Seminar
Time: Friday, June 19, 2pm New York time (8pm CEST)
Speaker: Boban Velickovic, University of Paris 7
Title: Strong guessing models
Abstract: The notion of a guessing model introduced by Viale and Weiss. The principle
GM(ω2,ω1) asserts that there are stationary many guessing models of size ℵ1 in Hθ, for all large enough regular θ. It follows from PFA and implies many of its structural consequences, however it does not settle the value of the continuum. In search of higher of forcing axioms it is therefore natural to look for extensions and higher versions of this principle. We formulate and prove the consistency of one such statement that we call SGM+(ω3,ω1).
It has a number of important structural consequences:

  • the tree property at ℵ2 and ℵ3
  • the failure of various weak square principles
  • the Singular Cardinal Hypothesis
  • Mitchell’s Principle: the approachability ideal agrees with the non stationary ideal on the set of cof(ω1) ordinals in ω2
  • Souslin’s Hypothesis
  • The negation of the weak Kurepa Hypothesis
  • Abraham’s Principles: every forcing which adds a subset of
    ω2 either adds a real or collapses some cardinals, etc.

The results are joint with my PhD students Rahman Mohammadpour.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, June 19, 1.30pm Toronto time (7.30pm CEST)
Speaker: David Schrittesser, University of Vienna
Title: Higher degrees of madness
Abstract: The notion of mad family can be generalized by replacing the finite ideal by an iterated Fubini product of the finite ideal. While these ideals are more complicated both combinatorially and in terms of Borel complexity, it turns out that the same assumptions of Ramsey theoretic regularity can rule out their existence. We sketch a proof of this and some related results. This talk is a sequel to my last talk at the Fields Institute Seminar.
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Online activities June 8 — June 14

June 9

Udine graduate course
Time:
 Tuesday, June 9, 10:00-12:00 CEST
Speaker: Vincenzo Dimonte, University of Udine
Title: Generalized Descriptive Set Theory II, Lecture 1
Abstract: The objective of the course is to prove an analogue of Silver’s Theorem for the space $2^\lambda$, where $\lambda$ is an uncountable cardinal of cofinality $\omega$, using some large cardinal strength (the proof is still unpublished).
This result has been chosen as an example to show, more in general, how to generalize a deep classical theorem in this setting, which properties of singular cardinals are useful in that respect, and what are the main obstacles of the generalization. The proof will use some peculiarities of singular cardinal combinatorics and some large cardinal strength, and everything will be introduced in the first three lessons. 
The course is self-contained (despite the name), the only prerequisite is to know basic set theory (the theory of forcing, the most basic descriptive set theory, maybe inaccessible cardinals).
The following is a tentative schedule:Tuesday 10.00-12.00 CEST, Friday 10.00-12.00 CEST, from 5 June 2020, for 5 lessons.
Lesson 1: Measurable cardinals
Lesson 2: Prikry forcing, diagonal Prikry forcing
Lesson 3: Strong Prikry condition, “double” diagonal Prikry forcing
Lesson 4: generalized G_0 dichotomy
Lesson 5: generalized Silver Theorem
Information: Via Microsoft Teams, to participate contact vincenzo.dimonte@uniud.it.

Münster Set Theory Seminar
Time: Tuesday, June 9, 4:15pm CEST
Speaker: Farmer Schlutzenberg
Title: Remarks on rank-into-rank embeddings
Abstract: Recall that Woodin’s large cardinal axiom I0 gives an ordinal λ and an elementary embedding j:L(V_{λ+1})→L(V_{λ+1}) with critical point <λ. Using methods due to Woodin, we show that if ZFC+I0 is consistent then so is ZF+DC(λ)+ there is an ordinal λ and an elementary j:V_{λ+2}→V_{λ+2}”. (A version with the added assumption that V_{λ+1}^sharp exists is due to the author, and Goldberg observed that the appeal to V_{λ+1}^sharp could actually be replaced by some further calculations of Woodin’s.)
Reference: https://arxiv.org/abs/2006.01077, “On the consistency of  ZF with an elementary embedding from V_{λ+2} into V_{λ+2}”.
Information: contact rds@wwu.de ahead of time in order to participate.

June 10

Bristol Logic and Set Theory Seminar (recurring lecture series)
Time:
 Wednesday, June 10, 14:00-15:30 UK time (15:00-16:30 CEST)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines IV
Abstract:
This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: Please contact Philip Welch (p.welch@bristol.ac.uk) ahead of time to participate.

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, June 10, 16:00-17:15 CEST
Speaker: Assaf Rinot
Title: Transformations of the transfinite plane
Abstract: We study the existence of transformations of the transfinite
plane that allow to reduce Ramsey-theoretic statements concerning
uncountable Abelian groups into classic partition relations for
uncountable cardinals. This is joint work with Jing Zhang.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, June 10, 16:15-17:45 UK time (17:15-18:45 CEST)
Speaker: Peter Holy, University of Udine
Title: Ideal and Tree Forcing Topologies
Abstract:
While the usual topology on the kappa-reals is based on the bounded ideal, in the sense that the basic open sets are generated by bounded partial functions from kappa to 2, we consider generalized topologies based on arbitrary ideals on kappa, in particular on the nonstationary ideal on regular and uncountable cardinals kappa. We will illustrate the connections of these topologies with certain tree forcing topologies, and in particular the connection of the nonstationary topology with the topology generated by kappa-Silver forcing. We will show how properties of this forcing notion carry over to properties of the nonstationary topology, and we will also generalize results on kappa-Silver forcing of Friedman, Khomskii and Kulikov. This is joint work with Marlene Koelbing, Philipp Schlicht and Wolfgang Wohofsky.
Information: Please login to the zoom meeting https://zoom.us/j/95916684321, if possible a few minutes before the talk.

CUNY Set Theory Seminar
Time: Wednesday, June 10, 7pm New York time (June 11, 1am CEST)
Speaker: Zachiri McKenzie
Title: Initial self-embeddings of models of set theory: Part II
Abstract: In the 1973 paper ‘Countable models of set theory’, H. Friedman’s investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of ‘initial segment’: transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman’s self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms ‘initial self-embeddings’. I will outline a proof of a refinement of H. Friedman’s Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman’s Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.​
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

June 12

Udine graduate course
Time:
 Friday, June 12, 10:00-12:00 CEST
Speaker: Vincenzo Dimonte, University of Udine
Title: Generalized Descriptive Set Theory II, Lecture 1
Abstract: The objective of the course is to prove an analogue of Silver’s Theorem for the space $2^\lambda$, where $\lambda$ is an uncountable cardinal of cofinality $\omega$, using some large cardinal strength (the proof is still unpublished).
This result has been chosen as an example to show, more in general, how to generalize a deep classical theorem in this setting, which properties of singular cardinals are useful in that respect, and what are the main obstacles of the generalization. The proof will use some peculiarities of singular cardinal combinatorics and some large cardinal strength, and everything will be introduced in the first three lessons. 
The course is self-contained (despite the name), the only prerequisite is to know basic set theory (the theory of forcing, the most basic descriptive set theory, maybe inaccessible cardinals).
The following is a tentative schedule:Tuesday 10.00-12.00 CEST, Friday 10.00-12.00 CEST, from 5 June 2020, for 5 lessons.
Lesson 1: Measurable cardinals
Lesson 2: Prikry forcing, diagonal Prikry forcing
Lesson 3: Strong Prikry condition, “double” diagonal Prikry forcing
Lesson 4: generalized G_0 dichotomy
Lesson 5: generalized Silver Theorem
Information: Via Microsoft Teams, to participate contact vincenzo.dimonte@uniud.it.

CUNY Set Theory Seminar
Time: Friday, June 12, 2pm New York time (8pm CEST)
Speaker: Michał Godziszewski — Munich Center for Mathematical Philosophy
Title: The Multiverse, Recursive Saturation and Well-Foundedness Mirage: Part II
Abstract:

Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust notion which has proved to be important for the study of nonstandard models (in particular, it is ubiquitous in the model theory of axiomatic theories of truth, e.g. in the topic of satisfaction classes, where one can show that if M models ZFC
and M is an ω-nonstandard model, then M admits a satisfaction class iff M is recursively saturated). V. Gitman and J. Hamkins showed in A Natural Model of the Multiverse Axioms that the collection of countable, recursively saturated models of set theory satisfy the so-called Hamkins’s Multiverse Axioms. The property that forces all the models in the Multiverse to be recursively saturated is the so-called Well-Foundedness Mirage axiom which asserts that every universe is ω-nonstandard from the perspective of some larger universe, or to be more precise, that: if a model M is in the multiverse then there is a model N in the multiverse such that M is a set in N and N models M is ω−nonstandard. Inspection of the proof led to a question if the recursive saturation could be avoided in the Multiverse by weakening the Well-Foundedness Mirage axiom. Our main results answer this in the positive. This is joint work with V. Gitman. T. Meadows and K. Williams.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, June 12, 1.30pm Toronto time (7.30pm CEST)
Speaker:TBA
Title: TBA
Abstract: TBA
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Online Activities June 1 — June 7 2020

June 1

Münster Set Theory Seminar
Time: Tuesday, June 1, 4:15pm CEST
Speaker: No seminar this week
Title: No seminar this week
Abstract: No seminar this week
Information: contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, June 2, 2:55pm New York time (20:55pm CEST)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact solecki@cornell.edu ahead of time to participate.

May 27

Jerusalem Set Theory Seminar
Time: Wednesday, June 3, 11:00am (Israel Time)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact omer.bn@mail.huji.ac.il ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, June 3, 16:00-17:15 CEST
Speaker: Colin Jahel
Title: In 2005, Kechris, Pestov and Todorcevic exhibited a correspondence
between combinatorial properties of structures and dynamical properties
of their automorphism groups. In 2012, Angel, Kechris and Lyons used
this correspondence to show the unique ergodicity of all the actions of
some groups. In this talk, I will give an overview of the aforementioned
results and discuss recent work generalizing results of Angel, Kechris
and Lyons.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, June 3, 14:00-15:30 (UK time)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines IV
Abstract: This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: Please contact Philip Welch (p.welch@bristol.ac.uk) ahead of time to participate.

CUNY Set Theory Seminar
Time: Wednesday, June 3, 7pm New York time (1am May 14 CEST)
Speaker: Zachiri McKenzie
Title: Initial self-embeddings of models of set theory: Part I
Abstract: In the 1973 paper ‘Countable models of set theory’, H. Friedman’s investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of ‘initial segment’: transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman’s self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms ‘initial self-embeddings’. I will outline a proof of a refinement of H. Friedman’s Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman’s Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.​
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Oxford Set Theory Seminar
Time: Wednesday, June 3, 4pm UK time
Speaker: TBA
Title: TBA
Abstract: TBA

Information: The seminar will take place virtually. Please email Sam Adam-Day at me@samadamday.com for the meeting id.

May 28

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, June 4, 16:00 CEST
Speaker: Stefan Hoffelner (University of Münster, North Rhine-Westphalia, Germany)
Title: Forcing the Sigma^1_3-separation property

Abstract: The separation property, introduced in the 1920s, is a classical notion in descriptive set theory. It is well-known due to Moschovakis, that Δ12-determinacy implies the Σ13-separation property; yet Δ12-determinacy implies an inner model with a Woodin cardinal. The question whether the Σ13-separation property is consistent relative to just ZFC remained open however since Mathias’ “Surrealist Landscape”-paper. We show that one can force it over L.
Information: Talk via zoom.

May 29

CUNY Set Theory Seminar
Time: Friday, June 5, 2pm New York time (8pm CEST)
Speaker: Michał Godziszewski — Munich Center for Mathematical Philosophy
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, June 5, 1.30pm Toronto time (7.30pm CEST)
Speaker:TBA
Title: TBA
Abstract: TBA
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Online activities May 25 — May 31 2020

May 26

Münster Set Theory Seminar
Time: Tuesday, May 26, 4:15pm CEST
Speaker: Liuzhen Wu, Chinese Acad. Sciences, Beijing
Title: BPFA and \Delta_1-definablity of NS_{\omega_1}​.
Abstract: I will discuss a proof of the joint consistency of​ BPFA and \Delta_1-definablity of NS_{\omega_1}. Joint work with Stefan Hoffelner and Ralf Schindler.
Information: contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, May 26, 2:55pm New York time (20:55pm CEST)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact solecki@cornell.edu ahead of time to participate.

May 27

Jerusalem Set Theory Seminar
Time: Wednesday, May 27, 11:00am (Israel Time)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact omer.bn@mail.huji.ac.il ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, May 27, 16:00-17:15 CEST
Speaker: Eliott Kaplan – University of Illinois at Urbana-Champaign
Title: Model completeness for the differential field of transseries with exponentiation
Abstract: I will discuss the expansion of the differential field of logarithmic-exponential transseries by its natural exponential function. This expansion is model complete and locally o-minimal. I give an axiomatization of the theory of this expansion that is effective relative to the theory of the real exponential field. These results build on Aschenbrenner, van den Dries, and van der Hoeven’s model completeness result for the differential field of transseries. My method can be adapted to show that the differential field of transseries with its restricted sine and cosine and its unrestricted exponential is also model complete and locally o-minimal.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, May 27, 14:00-15:30 (UK time)
Speaker: Philip Welch, University of Bristol
Title: Higher type recursion for Infinite time Turing Machines IV
Abstract: This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: Please contact Philip Welch (p.welch@bristol.ac.uk) ahead of time to participate.

CUNY Set Theory Seminar
Time: Wednesday, May 27, 7pm New York time (1am May 14 CEST)
Speaker: Bartosz Wcisło, University of Warsaw
Title: Tarski boundary II
Abstract: Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PA) we add a unary predicate T(x) with the intended interpretation ‘x is a (code of a) true sentence.’ Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour. One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate ‘strong’ in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this ‘demarcating line’ between conservative and non-conservative truth theories ‘the Tarski boundary.’ Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PA or exactly equivalent to the principle of global reflection over PA. It says that sentences provable in PA are true in the sense of the predicate T. This in turn is equivalent to Δ0-induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of ‘Tarski boundary’ presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Oxford Set Theory Seminar
Time: Wednesday, May 27, 4pm UK time
Speaker: Ali Enayat, Gothenberg
Title: Leibnizian and anti-Leibnizian motifs in set theory
Abstract: Leibniz’s principle of identity of indiscernibles at first sight appears completely unrelated to set theory, but Mycielski (1995) formulated a set-theoretic axiom nowadays referred to as LM (for Leibniz-Mycielski) which captures the spirit of Leibniz’s dictum in the following sense: LM holds in a model M of ZF iff M is elementarily equivalent to a model M* in which there is no pair of indiscernibles. LM was further investigated in a 2004 paper of mine, which includes a proof that LM is equivalent to the global form of the Kinna-Wagner selection principle in set theory. On the other hand, one can formulate a strong negation of Leibniz’s principle by first adding a unary predicate I(x) to the usual language of set theory, and then augmenting ZF with a scheme that ensures that I(x) describes a proper class of indiscernibles, thus giving rise to an extension ZFI of ZF that I showed (2005) to be intimately related to Mahlo cardinals of finite order. In this talk I will give an expository account of the above and related results that attest to a lively interaction between set theory and Leibniz’s principle of identity of indiscernibles.

May 28

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, May 28, 16:00 CEST
Speaker: Diego Mejía, Shizuoka University, Japan
Title: Preserving splitting families
Abstract: We present a method to force splitting families that can be preserved by a large class of finite support iterations of ccc posets. As an application, we show how to force several cardinal characteristics of the continuum to be pairwise different.
Information: Talk via zoom.

May 29

CUNY Set Theory Seminar
Time: Friday, May 29, 2pm New York time (8pm CEST)
Speaker: Kameryn Williams University of Hawaii at Mānoa
Title: The geology of inner mantles
Abstract: An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let’s call the inner models in this sequence the inner mantles.
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, May 29, 1.30pm Toronto time (7.30pm CEST)
Speaker:TBA
Title: TBA
Abstract: TBA
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Udine online activities
Time: Friday, May 29, 16:30-18:30 CEST
Speaker: Peter Holy, University of Udine
Title: Generalized topologies on 2^kappa, Silver forcing, and the diamond principle
Abstract:I will talk about the connections between topologies on 2^kappa induced by ideals on kappa and topologies on 2^kappa induced by certain tree forcing notions, highlighting the connection of the topology induced by the nonstationary ideal with kappa-Silver forcing. Assuming that Jensen’s diamond principle holds at kappa, we then generalize results on kappa-Silver forcing of Friedman, Khomskii and Kulikov that were originally shown for inaccessible kappa: In particular, I will present a proof that also in our situation, kappa-Silver forcing satisfies a strong form of Axiom A. By a result of Friedman, Khomskii and Kulikov, this implies that meager sets are nowhere dense in the nonstationary topology. If time allows, I will also sketch a proof of the consistency of the statement that every Delta^1_1 set (in the standard bounded topology on 2^kappa) has the Baire property in the nonstationary topology, again assuming the diamond principle to hold at kappa (rather than its inaccessibility). This is joint work with Marlene Koelbing, Philipp Schlicht and Wolfgang Wohofsky.
Information: Via Microsoft Teams, to participate contact vincenzo.dimonte@uniud.it

Online activities May 18 — May 22 2020

May 19

Münster Set Theory Seminar
Time: Tuesday, May 12, 4:15pm CEST
Speaker: Stefan Hoffelner, University of Muenster
Title: Forcing the $\bf{\Sigma^1_3}$-separation property.
Abstract: The separation property, introduced in the 1920s, is a classical notion in descriptive set theory. It is well-known due to Moschovakis, that $\bf{\Delta^1_2}$-determinacy implies the $\bf{\Sigma^1_3}$-separation property; yet $\bf{\Delta^1_2}$-determinacy implies an inner model with a Woodin cardinal. The question whether the $\bf{\Sigma^1_3}$-separation property is consistent relative to just ZFC remained open however since Mathias’ „Surrealist Landscape“-paper from 1968. We show that one can force it over L.
Information: contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, May 19, 2:55pm New York time (20:55pm CEST)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact solecki@cornell.edu ahead of time to participate.

May 20

Jerusalem Set Theory Seminar
Time: Wednesday, May 20, 11:00am (Israel Time)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: contact omer.bn@mail.huji.ac.il ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, May 13, 16:00-17:15 CEST
Speaker: Michael Hrusak, Universidad Nacional Autónoma de México
Title: Strong measure zero in Polish groups (joint with W. Wohofsky, J. Zapletal and/or O. Zindulka)
Abstract: We study the extent to which the Galvin-Mycielski-Solovay
characterization of strong measure zero subsets of the real line
extends to arbitrary Polish group. In particular, we show that
an abelian Polish group satisfies the GMS characterization if and only
if it is locally compact. We shall also consider the non-abelian case,
and discuss the use and existence of invariant submeasures on Polish groups.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, May 20, 14:00-15:30 (UK time)
Speaker: Philip Welch (University of Bristol)
Title: Higher type recursion for infinite time Turing machines IV
Abstract: This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: Please contact Philip Welch (p.welch@bristol.ac.uk) ahead of time to participate.

CUNY Set Theory Seminar
Time: Wednesday, May 20, 7pm New York time (1am May 14 CEST)
Speaker: TBA
Title: TBA
Abstract: TBA
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Oxford Set Theory Seminar
Time: Wednesday, May 20, 4pm UK time
Speaker: Joel David Hamkins, OXFORD
Title: Bi-interpretation of weak set theories
Abstract: Set theory exhibits a truly robust mutual interpretability phenomenon: in any model of one set theory we can define models of diverse other set theories and vice versa. In any model of ZFC, we can define models of ZFC + GCH and also of ZFC + ¬CH and so on in hundreds of cases. And yet, it turns out, in no instance do these mutual interpretations rise to the level of bi-interpretation. Ali Enayat proved that distinct theories extending ZF are never bi-interpretable, and models of ZF are bi-interpretable only when they are isomorphic. So there is no nontrivial bi-interpretation phenomenon in set theory at the level of ZF or above.  Nevertheless, for natural weaker set theories, we prove, including ZFC- without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. Specifically, there are well-founded models of ZFC- that are bi-interpretable, but not isomorphic—even (H(\omega_1),\in) and (H(\omega_2),\in) can be bi-interpretable—and there are distinct bi-interpretable theories extending ZFC-. Similarly, using a construction of Mathias, we prove that every model of ZF is bi-interpretable with a model of Zermelo set theory in which the replacement axiom fails. This is joint work with Alfredo Roque Freire.
Information: The seminar will take place virtually. Please email Samuel Adam-Day (me@samadamday.com) for the meeting id.

May 21

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, May 21, 16:00 CEST
Speaker: TBA
Title: TBA
Abstract: TBA
Information: Talk via zoom.

May 22

CUNY Set Theory Seminar
Time: Friday, May 22, 2pm New York time (8pm CEST)
Speaker: Ali Enayat, University of Gothenburg
Title: Recursively saturated models of set theory and their close relatives: Part II
Abstract: A model M of set theory is said to be ‘condensable’ if there is an ‘ordinal’ α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus ‘there is an inaccessible cardinal’, there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of ‘ordinals’ α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, May 22, 1.30pm Toronto time (7.30pm CEST)
Speaker: Vinicius de Oliveira Rodrigues, University of São Paulo and University of São Paulo, Institute of Mathematics and Statistics
Title: Pseudocompact hyperspaces of Isbell-Mrówka spaces
Abstract: J. Ginsburg has asked what is the relation between the pseudocompactness of the ω-th power of a topological space Xand the pseudocompactness of its Vietoris Hyperspace, exp(X). M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form Ψ(A) where A is an almost disjoint family. Regarding these spaces, if exp(X) is pseudocompact, then Xω is also pseudocompact, and Xω is pseudocompact iff A is a MAD family. They showed that if the cardinal characteristic 𝔭 is 𝔠, then for every MAD family A, exp(Ψ(A)) is pseudocompact, and if the cardinal characteristic 𝔥 is less than 𝔠, there exists a MAD family A such that exp(Ψ(A)) is not pseudocompact. They asked if there exists a MAD family A (in ZFC) such that exp(Ψ(A)) is pseudocompact.
In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.
Information: The seminar will take place virtually. ZOOM ID: https://yorku.zoom.us/j/96087161597

Online activities May 11 — May 17 2020

May 12

Münster Set Theory Seminar
Time: Tuesday, May 12, 4:15pm CEST
Speaker: Farmer Schlutzenberg, University of Muenster
Title: $j:V_\delta\to V_\delta$ in $L(V_\delta)$
Abstract: Assuming $\mathrm{ZF}+V=L(V_\delta)$ where $\delta$ is a
limit ordinal of uncountable cofinality, we show there is no
non-trivial $\Sigma_1$-elementary $j:V_\delta\to V_\delta$. Reference:
Section 8 of “Reinhardt cardinals and non-definability”, arXiv
2002.01215.
Information: contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, May 12, 2:55pm New York time (20:55pm CEST)
Speaker: Konstantin Slutsky, University of Paris 7
Title: Smooth Orbit equivalence relation of free Borel R^d-actions
Abstract: Smooth Orbit Equivalence (SOE) is an orbit equivalence relation between free ℝd-flows that acts by diffeomorphisms between orbits. This idea originated in ergodic theory of ℝ-flows under the name of time-change equivalence, where it is closely connected with the concept of Kakutani equivalence of induced transformations. When viewed from the ergodic theoretical viewpoint, SOE has a rich structure in dimension one, but, as discovered by Rudolph, all ergodic measure-preserving ℝd-flows, d > 1, are SOE. Miller and Rosendal initiated the study of this concept from the point of view of descriptive set theory, where phase spaces of flows aren’t endowed with any measures. This significantly enlarges the class of potential orbit equivalences, and they proved that all nontrivial free Borel ℝ-flows are SOE. They posed a question of whether the same remains to be true in dimension d>1. In this talk, we answer their question in the affirmative, and show that all nontrivial Borel ℝd-flows are SOE.
Information: contact solecki@cornell.edu ahead of time to participate.

May 13

Jerusalem Set Theory Seminar
Time: Wednesday, May 13, 11:00am (Israel Time)
Speaker: Alejandro Poveda (Universitat de Barcelona)
Title: Sigma-Prikry forcings and their iterations (Part II)
Abstract:In the previous talk, we introduced the notion of \Sigma-Prikry forcing and showed that many classical Prikry-type forcing which center on countable cofinalities fall into this framework.
The aim of this talk is to present our iteration scheme for \Sigma-Prikry forcings.
In case time permits, we will also show how to use this general iteration theorem to derive as a corollary the following strengthening of Sharon’s theorem: starting with \omega-many supercompact cardinals one can force a generic extension where Refl(<\omega,\kappa^+) holds and the SCH_\kappa fails, for \kappa being a strong limit cardinal with cofinality \omega
Information: contact omer.bn@mail.huji.ac.il ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, May 13, 16:00-17:15 CEST
Speaker: Caroline Terry (University of Chicago)
Title: Speeds of hereditary properties and mutual algebricity
(joint work with Chris Laskowski.)
Abstract: A hereditary graph property is a class of finite graphs closed under isomorphism and induced subgraphs. Given a hereditary graph property H, the speed of H is the function which sends an integer n to the number of distinct elements in H with underlying set {1,…,n}. Not just any function can occur as the speed of hereditary graph property. Specifically, there are discrete “jumps” in the possible speeds. Study of these jumps began with work of Scheinerman and Zito in the 90’s, and culminated in a series of papers from the 2000’s by Balogh, Bollob\'{a}s, and Weinreich, in which essentially all possible speeds of a hereditary graph property were characterized. In contrast to this, many aspects of this problem in the hypergraph setting remained unknown. In this talk we present new hypergraph analogues of many of the jumps from the graph setting, specifically those involving the polynomial, exponential, and factorial speeds. The jumps in the factorial range turned out to have surprising connections to the model theoretic notion of mutual algebricity, which we also discuss.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Bristol Logic and Set Theory Seminar
Time:
 Wednesday, May 13, 14:00-15:30 (UK time)
Speaker: Philip Welch (University of Bristol)
Title: Higher type recursion for infinite time Turing machines III
Abstract:This is part of a series informal working seminars on an extension of Kleene’s early 1960’s on recursion in higher types. (This formed a central theme on the borders of set theory and recursion theory in the 60’s and early 70’s, although now unfortunately not much discussed. Amongst the main names here were Gandy, Aczel, Moschovakis, Harrington, Normann.) We aim to present a coherent version of type-2 recursion for the infinite time Turing machine model. We aim to be somewhat (but not entirely) self-contained. Basic descriptive set theory, and recursion theory, together with admissibility theory will be assumed.
Information: Please contact Philip Welch (p.welch@bristol.ac.uk) ahead of time to participate.

CUNY Set Theory Seminar
Time: Wednesday, May 13, 7pm New York time (1am May 14 CEST)
Speaker: Laurence Kirby, CUNY
Title: Bounded finite set theory
Abstract: There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic IΔ0? I propose a candidate for such a theory, called IΔ0S, and consider the questions: what set-theoretic axioms can it prove? And given a model M of IΔ0 is there a model of IΔ0S whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

May 14

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, May 14, 16:00 CEST
Speaker: Andrew Brooke Taylor, University of Leeds (UK)
Title: Product of CW complexes
Abstract: CW spaces are often presented as the “spaces of choice” in algebraic topology courses, being relatively nice spaces built up by successively gluing on Euclidean balls of increasing dimension. However, the product of CW complexes need not be a CW complex, as shown by Dowker soon after CW complexes were introduced. Work in the 1980s characterised when the product is a CW complex under the assumption of CH, or just b=ℵ1. In this talk I will give and prove a complete characterisation of when the product of CW complexes is a CW complex, valid under ZFC. The characterisation however involves b; the proof is point-set-topological (I won’t assume any knowledge of algebraic topology) and uses Hechler conditions.
Information: Talk via zoom.

May 15

CUNY Set Theory Seminar
Time: Friday, May 15, 2pm New York time (8pm CEST)
Speaker: Ali Enayat, University of Gothenburg
Title: Recursively saturated models of set theory and their close relatives: Part I
Abstract: A model M of set theory is said to be ‘condensable’ if there is an ‘ordinal’ α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus ‘there is an inaccessible cardinal’, there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of ‘ordinals’ α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online activities May 4 — May 10 2020

May 5

Münster Set Theory Seminar
Time: Tuesday, May 5, 4:15pm CEST
Speaker: Andreas Lietz, University of Muenster
Title: How to force (*) from less than a supercompact
Abstract: Asperò-Schindler have shown that Woodin’s axiom (*) is a consequence of MM^{++} and the latter is known to be forceable from a supercompact cardinal. (*) however has consistency strength of \omega-many Woodin cardinals, so it should be possible to force it from a much weaker assumption. We present a construction that does so from strictly less than a \kappa^{+++}-supercompact cardinal \kappa (+GCH). The strategy will be to iterate the forcing from the proof of MM^{++}\Rightarrow(\ast). Two main difficulties arise: Whenever we want to use that forcing we will have to make sure that it is semiproper and that NS_{\omega_1} is saturated. We hope that the large cardinal assumption can be lowered to around the region of an inaccessible limit of Woodin cardinals. This is joint work with Ralf Schindler.
Information: The seminar will be held remotely via zoom. Please contact rds@wwu.de ahead of time in order to participate.

Cornell Logic Seminar
Time: Tuesday, May 5, 2:55pm New York time (20:55pm CEST)
Speaker: Andrew Zucker, University of Lyon
Title: Topological dynamics beyond Polish groups
Abstract: When G is a Polish group, one way of knowing that G has “nice” dynamics is to show that M(G), the universal minimal flow of G, is metrizable. However, works of Bartosova, Gheysens, and Krupinski–Pillay investigate groups beyond the Polish realm, such as Sym(κ), Homeo(ω1), and automorphism groups of uncountable, ω-homogeneous structures. For example, Bartosova shows that the universal minimal flow of Sym(κ) is the space of linear orders on κ–not a metrizable space, but still “nice.” In this talk, we seek to put these results into a general framework which encompasses all topological groups.
This is joint work with Gianluca Basso

May 6

Paris-Lyon Séminaire de Logique
Time:
 Wednesday, May 6, 16:00-17:15 CEST
Speaker: Ilijas Farah – York University (Toronto)
Title: Between ultrapowers and reduced products.
Abstract: Ultrapowers and reduced powers are two popular tools for studying countable (and separable metric) structures. Once an ultrafilter on N is fixed, these constructions are functors into the category of countably saturated structures of the language of the original structure. The question of the exact relation between these two functors has been raised only recently by Schafhauser and Tikuisis, in the context of Elliott’s classification programme. Is there an ultrafilter on N such that the quotient map from the reduced product associated with the Fréchet filter onto the ultrapower has the right inverse? The answer to this question involves both model theory and set theory. Although these results were motivated by the study of C*-algebras, all of the results and proofs will be given in the context of classical (discrete) model theory.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Oxford Set Theory Seminar
Time:
 Wednesday, May 6, 16:00-17:30 UK time (17:00-18:30 CEST)
Speaker: Victoria Gitman, City University of New York
Title: Elementary embeddings and smaller large cardinals
Abstract: A common theme in the definitions of larger large cardinals is the existence of elementary embeddings from the universe into an inner model. In contrast, smaller large cardinals, such as weakly compact and Ramsey cardinals, are usually characterized by their combinatorial properties such as existence of large homogeneous sets for colorings. It turns out that many familiar smaller large cardinals have elegant elementary embedding characterizations. The embeddings here are correspondingly ‘small’; they are between transitive set models of set theory, usually the size of the large cardinal in question. The study of these elementary embeddings has led us to isolate certain important properties via which we have defined robust hierarchies of large cardinals below a measurable cardinal. In this talk, I will introduce these types of elementary embeddings and discuss the large cardinal hierarchies that have come out of the analysis of their properties. The more recent results in this area are a joint work with Philipp Schlicht.
Information: For the Zoom access code, contact Samuel Adam-Day: me@samadamday.com.

May 7

Kurt Gödel Research Center Seminar (organised by Ben Miller)
Time:
 Thursday, May 7, 16:00 CEST
Speaker: Stefan Hoffelner, University of Muenster
Title: TBA
Abstract: TBA
Information: Talk via zoom.

May 8

Toronto Set Theory Seminar
Time: Friday, May 8, 1:30-3:00pm EDT (19:30-21:00 CEST)
Speaker: Dima Sinapova, University of Chicago
Title: Iteration, reflection, and Prikry forcing
Abstract: There is an inherent tension between stationary reflection and the failure of SCH. The former is a compactness type principle that follows from large cardinals. The latter is an instance of incompactness, and usually obtained using Prikry forcing. We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.
Information: The talk will take place via zoom: https://yorku.zoom.us/j/96087161597.

CUNY Set Theory Seminar
Time: Friday, May 8, 2pm New York time (8pm CEST)
Speaker: Sandra Mueller, KGRC Vienna
Title: How to obtain lower bounds in set theory
Abstract: Computing the large cardinal strength of a given statement is one of the key research directions in set theory. Fruitful tools to tackle such questions are given by inner model theory. The study of inner models was initiated by Gödel’s analysis of the constructible universe L. Later, it was extended to canonical inner models with large cardinals, e.g. measurable cardinals, strong cardinals or Woodin cardinals, which were introduced by Jensen, Mitchell, Steel, and others.
We will outline two recent applications where inner model theory is used to obtain lower bounds in large cardinal strength for statements that do not involve inner models. The first result, in part joint with J. Aguilera, is an analysis of the strength of determinacy for certain infinite two player games of fixed countable length, and the second result, joint with Y. Hayut, involves combinatorics of infinite trees and the perfect subtree property for weakly compact cardinals κ. Finally, we will comment on obstacles, questions, and conjectures for lifting these results higher up in the large cardinal hierarchy.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.