# Online activities 16-22 May

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

Helsinki Logic Seminar, Special lecture
Time: Monday, 16 May, 12:00 – 14:00 Helsinki time (11:00-13:00 CEST)
Speaker: Philip Welch, University of Bristol
Title: Quasi-Inductive Definitions
Abstract: Such definitions extend the well researched theory of monotone inductive definitions by allowing non-monotone processes that are structured by liminf rules at limits rather than simple unions. Much of the Moschovakian theory of induction over abstract structures can be performed in this context, resulting in certain Spector classes of sets. Whereas the theory of inductive definitions leads to the idea of the least admissible set over a structure A, here one constructs the least ‘strongly Sigma_2-admissible set’ over A. Just as Sigma^0_1-Determinacy is associated with HYP(N), and Kleene’s higher type recursion, so there are connections to be explored here with a higher type form of quasi-inductive recursion for a q-HYP(N).
Information: The talk will take place in hybrid format. Please see the seminar webpage for login information.

Leeds Models and Sets Seminar
Time: Tuesday, 17 May, 13:45-14:55 UK time (14:45-15:55 CEST)
Speaker: Julia Knight, University of Notre Dame
Title: Freeness and typical behavior for algebraic structures
Abstract: The talk is on joint work with Johanna Franklin and Turbo Ho.  Gromov asked “What is a typical group?”  He was thinking of finitely presented groups.  He proposed an approach involving limiting density.  In 2013, I conjectured that for elementary first order sentences $\varphi$, and for group presentations with n generators ($n\geq 2$) and a single relator, the limiting density for groups satisfying $\varphi$ always exists, with value 0 or 1, and the value is 1 iff $\varphi$ is true in the non-Abelian free groups.  The conjecture is still open, but there are positive partial results by Kharlampovich and Sklinos, and by Coulon, Ho, and Logan.  We ask Gromov’s question about structures in other equational classes, or \emph{algebraic varieties} in the sense of universal algebra.  We give examples illustrating different possible behaviors.  Focusing on languages with just finitely many unary function symbols, we prove a result with conditions sufficient to guarantee that the analogue of the conjecture holds.  The proof uses a version of Gaifman’s Locality Theorem, plus ideas from random group theory and probability.
Information: Please see the seminar webpage.

KGRC Set Theory Seminar, Vienna
Time: Tuesday, 17 May, 15:00-16:30 CEST
Speaker: Philipp Lücke, University of Barcelona
Title: Patterns in the large cardinal hierarchy
Abstract: In my talk, I will present results showing that the existence of various well-known large cardinals can be characterized through the validity of strong extensions of the downward Löwenheim-Skolem theorem.
These equivalences show that certain patterns recur throughout the large cardinal hierarchy.
In particular, they show that strongly unfoldable cardinals, introduced by Villaveces in his model-theoretic investigations of models of set theory, relate to subtle cardinals, introduced by Kunen and Jensen in their studies of strong diamond principles, in the same way as supercompact cardinals relate to Vopěnka cardinals and strong cardinals relate to Woodin cardinals.
This is joint work in progress with Joan Bagaria (Barcelona).
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 18 May, 14:00-16:00 Israel Time (13:00-15:00 CEST)
Speaker: Shaun Allison
Title: Polish groups with the pinned property, part 2
Abstract: We will discuss a property of Polish groups called the “pinned property” which means that every orbit equivalence relation they generate is “pinned”, a metamathematical notion which is used to separate the complexity of different equivalence relations up to Borel reducibility. We will discuss the subtle way that the amount of choice assumed influences the pinned property. In particular, we will discuss results of Su Gao and Alex Thompson which imply that in a mode of ZFC, a Polish group has the pinned property if and only if it has a complete compatible left-invariant metric. We will also present a new result which, along with a result of Larson-Zapletal, implies that in the Solovay model derived from a measurable, a Polish group has the pinned property if and only if it involves S_\infty (caveat: for the special case of non-Archimedian groups). Time permitting, we will discuss Larson-Zapletal’s result as well. This is part of a larger project to measure and categorize the “classification strength” of Polish groups.
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the seminar announcement and zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 18 May, 16:00-17:30 CEST
Speaker: Laura Fontanella, Creteil University
Title: Representing ordinals in classical realizability
Abstract: Realizability aims at extracting the computational content of mathematical
proofs. Introduced in 1945 by Kleene as part of a broader program in constructive
mathematics, realizability has later evolved to include classical logic and even set theory.
Krivine’s work led to define realizability models for the theory ZF following a technique
that generalizes the method of Forcing. After a brief presentation of this technique, we
will discuss the problem of representing ordinals in realizability models for set theory,
thus we will present the solution proposed in a joint work with Guillaume Geoffroy that
led to realize uncountable versions of the Axiom of Dependent Choice.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 18 May, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Aristotelis Panagiotopoulos, CMU
Title: Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension
Abstract: For every Polish permutation group P≤Sym⁡(N), let A↦[A]P be the assignment which maps every A⊆N to the set of all k∈N whose orbit under the action of the stabilizer PF of some finite F⊆A is finite. Then A↦[A]P is a closure operator and hence it endows P with a natural notion of dimension dim(P)dim⁡(P). This notion of dimension has been extensively studied in model theory when A↦[A]P satisfies additionally the exchange principle, that is, when A↦[A]P forms a pregeometry. However, under the exchange principle, every Polish permutation group P with dim⁡(P)<∞ is locally compact and therefore unable to generate any “wild” dynamics. In this talk, we will discuss the relationship between dim⁡(P) and certain strong ergodicity phenomena in the absence of the exchange principle. In particular, for every n∈N, we will provide a Polish permutation group P with dim⁡(P)=n whose Bernoulli shift P↷RN is generically ergodic relative to the injective part of the Bernoulli shift of any permutation group Q with dim⁡(Q)<n. We will use this to exhibit an equivalence relation of pinned cardinal ℵ1 which strongly resembles Zapletal’s counterexample to a question of Kechris, but which does not Borel reduce to the latter. Our proofs rely on the theory of symmetric models of choiceless set theory and in the process we establish that a vast collection of symmetric models admit a theory of supports similar to the basic Cohen model. This is joint work with Assaf Shani.
Information: Please see the seminar webpage.

KGRC Logic Colloquium, Vienna
Time:
Thursday, 19 May, 15:00 – 15:45 CET
Speaker: Corey Switzer, University of Vienna
Title: Axiomatizing Kaufmann Models of Arithmetic in Strong Logics
Abstract: A Kaufmann model of PA is an ω1-like, recursively saturated, rather classless model (these terms will be defined in the talk). Such models have been an important object of study in model theory of arithmetic and its environs since the 70’s. Kaufmann models are natural counterexamples to several theorems about countable models of PA holding at the uncountable. Moreover they are a witness to incompactness at ω1 similar to an Aronszajn tree. The proof that Kaufmann models exist lies along a somewhat twisted road. Kaufmann showed that there are Kaufmann models under the combinatorial principle ♢ω1 and, later, Shelah eliminated the use of ♢ω1 by appealing to a forcing absoluteness argument involving the strong logic Lω1,ω(Q) where Q is the quantifier “there exists uncountably many”. It remains an extremely interesting, if somewhat vague, question, attributed to Hodges, whether one can build a Kaufmann model “by hand” in ZFC without appealing to generic absoluteness.
In this talk we will report on our recent progress in this area. Specifically we will consider the role that the strong logic Lω1,ω(Q)plays in Kaufmann models and show that the statement “Kaufmann models can be axiomatized by Lω1,ω(Q)” is independent of ZFC. Along the way we will discuss how Kaufmann models are affected by forcing and in particular show that it is independent of ZFC whether or not there is a Kaufmann model which can be “killed” by forcing without collapsing ω1.
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 20 May, 16.00-18.00 CEST
Speaker: A. Marcone, University of Udine
Title: The transfinite Ramsey theorem
Abstract: In this talk I discuss generalizations of the classic finite Ramsey theorem that substitute “set of cardinality n” with the notion of alpha-large set, where alpha is a countable ordinal. The prototype of these results is the statement that Paris and Harrington showed unprovable in PA in 1977. Since then several extensions were proved, typically for ordinals up to epsilon_0. Our results extend this approach by dealing with ordinals (at least) up to Gamma_0 and using simultaneously alpha-large sets (almost) everywhere in the statements. Quite surprisingly, in many cases we obtain tight bounds on the generalized Ramsey numbers, in contrast with the classical finite case where tight bounds are known only for very few cases involving very small numbers. This is joint work with Antonio Montalbán.
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, 20 May, 12:30pm New York time (18:30 CEST)
Speaker: William Chan, Carnegie Mellon University
Title: Determinacy and Partition Properties
Abstract: In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

# Informal set theory workshop, Barcelona 12.+13. May

On the 12th and 13th of May, the “Barcelona Research Group on Set Theory” (BCNSETS) will be holding an informal in-person workshop, and everyone interested is cordially invited to participate. The following presentations are currently planned:

Thursday 12. May (Seminar room S2, Facultat de Matemàtiques i Informàtica):
10:30-12:00 Philipp Luecke (Barcelona)
12:30-14:00 Juan Carlos Martínez (Barcelona)
16:00-17:30 Jeffrey Bergfalk (Barcelona)

Friday 13. May (Seminar room IF, Facultat de Matemàtiques i Informàtica):
10:30-12:00 Joan Bagaria (Barcelona)
12:30-14:00 Martina Iannella (Udine)

16:00-17:30 Claudio Ternullo (Barcelona)

If you have any questions regarding this meeting, please feel free to contact Philipp Luecke (philipp.luecke@ub.edu).

# Online activities 9-15 May

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

Leeds Models and Sets Seminar
Time: Tuesday, 10 May, 13:45-14:55 UK time (14:45-15:55 CEST)
Speaker: Diana Carolina Montoya, University of Vienna
Title: tba
Abstract: tba
Information: Please see the seminar webpage.

KGRC Set Theory Seminar, Vienna
Time: Tuesday, 10 May, 15:00-16:30 CEST
Speaker: Ö. Bag, Universität Wien
Title: On higher Baire spaces combinatorics
Abstract: In this talk we will consider some recent results regarding the higher Baire spaces analogues of the almost disjointness, bounding, dominating and splitting numbers. In particular, we will discuss the recently established relative consistency of s(κ)=κ+<b(κ) for κ-strongly unfoldable, the relative consistency of κ+<a(κ)=b(κ)<d(κ)<c(κ) for κ regular uncountable, as well as the global evaluation of the spectrum of κ-mad families.
The results build to a great extent on the method of non-linear iterations of Cumming-Shelah, the method of matrix iterations as originally appearing in the work on the ultrafilter and dominating numbers of Blass-Shelah and its subsequent developments, and give (among others) an interesting application of Kunen’s isomorphism of names argument in the context of Easton forcing. We will conclude the talk with a brief discussion of remaining open questions.
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 11 May, 14:00-16:00 Israel Time (13:00-15:00 CEST)
Speaker: Shaun Allison
Title: Polish groups with the pinned property
Abstract: We will discuss a property of Polish groups called the “pinned property” which means that every orbit equivalence relation they generate is “pinned”, a metamathematical notion which is used to separate the complexity of different equivalence relations up to Borel reducibility. We will discuss the subtle way that the amount of choice assumed influences the pinned property. In particular, we will discuss results of Su Gao and Alex Thompson which imply that in a mode of ZFC, a Polish group has the pinned property if and only if it has a complete compatible left-invariant metric. We will also present a new result which, along with a result of Larson-Zapletal, implies that in the Solovay model derived from a measurable, a Polish group has the pinned property if and only if it involves S_\infty (caveat: for the special case of non-Archimedian groups). Time permitting, we will discuss Larson-Zapletal’s result as well. This is part of a larger project to measure and categorize the “classification strength” of Polish groups.
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the seminar announcement and zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 11 May, 16:00-17:30 CEST
Speaker: Sandra Müller, TU Wien
Title: Inner Models, Determinacy, and Sealing
Abstract: Inner model theory has been very successful in connecting determinacy axioms to the existence of inner models with large cardinals and other natural hypotheses. Recent results of Larson, Sargsyan, and Trang suggest that a Woodin limit of Woodin cardinals is a natural barrier for our current methods to prove these connections. One reason for this comes from Sealing, a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. Woodin showed in his famous Sealing Theorem that in the presence of a proper class of Woodin cardinals Sealing holds after collapsing a supercompact cardinal. I will outline the importance of Sealing and discuss a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of Sealing from iterability. This is joint work with Grigor Sargsyan and Bartosz Wcisło.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 11 May, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Rehana Patel, African Institute for Mathematical Sciences
Title: The number of ergodic models of an infinitary sentence
Abstract: Given an Lω1ω-sentence φ in a countable language, we call an ergodic S∞-invariant probability measure on the Borel space of countable models of φ (having fixed underlying set) an ergodic model of φ. I will discuss the number of ergodic models of such a sentence φ, including the case when φ is a Scott sentence. This is joint work with N. Ackerman, C. Freer, A. Kruckman and A. Kwiatkowska.
Information: Please see the seminar webpage.

Cross-Alps Logic Seminar
Time: Friday, 13 May, 16.00-18.00 CEST
Speaker: U. Darji, University of Louisville
Title: Descriptive complexity and local entropy
Abstract: Blanchard introduced the concepts of Uniform Positive Entropy (UPE) and Complete Positive Entropy (CPE) as topological analogues of K-automorphism. He showed that UPE implies CPE, and that the converse is false. A flurry of recent activity studies the relationship between these two notions. For example, one can assign a countable ordinal which measures how complicated a CPE system is. Recently, Barbieri and García-Ramos constructed Cantor CPE systems at every level of CPE. Westrick showed that natural rank associated to CPE systems is actually a \Pi^1_1-rank. More importantly, she showed that the collection of CPE Z2-SFT’s is a \Pi^1_1-complete set. In this talk, we discuss some results, where UPE and CPE coincide and others where we show that the complexity of certain classes of CPE systems is \Pi^1_1-complete. This is joint work with García-Ramos.
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, 13 May, 12:30pm New York time (18:30 CEST)
Speaker: Andrew Brooke-Taylor, University of Leeds
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, 13 May, 13.30-15.00 Toronto time (19.30-21.00 CEST)
Title: Lindelöf Σ-spaces in 2022
Abstract: This talk is a survey and an advertisement of the theory of Lindelöf Σ-spaces. We will present ten equivalent definitions of the Lindelöf Σ-property and a selection of results that have numerous applications in General Topology, Topological Algebra and Cp-theory.

# PhD course on model companionship by Matteo Viale starting Tuesday

Matteo Viale will run a PhD course on model companionship results for set theory. The course will be in Turin and starts Tuesday 3rd of May 16.30 italian time. The course can be followed online on the platform Webex. All infos on the course including tentative program and schedule can be found here:

http://torino.logicgroup.altervista.org/torino/courses.php?lng=eng#

# Online activities 2-8 May

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

Leeds Models and Sets Seminar
Time: Tuesday, 3 May, 13:45-14:55 UK time (14:45-15:55 CEST)
Speaker: Noa Lavi, Hebrew University of Jerusalem
Title: tba
Abstract: tba
Information: Please see the seminar webpage.

KGRC Set Theory Seminar, Vienna
Time: Tuesday, 3 May, 15:00-16:30 CEST
Speaker: M. A. Cardona Montoya, TU Wien
Title: On the cardinal characteristics associated with \varepsilon
Abstract: Let ε be the σ-ideal generated by closed measure zero sets of reals. We prove that, for ε, their associated cardinal characteristics (i.e. additivity, covering, uniformity and cofinality) are pairwise different.
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

Helsinki Logic Seminar
Time: Wednesday, 4 May, 12:00 – 14:00 Helsinki time (11:00-13:00 CEST)
Speaker: Philip Welch, University of Bristol
Title: Free subsets of structures
Abstract: If A is a first order structure, a subset X of dom(A) is free if no element of X can be defined in A from other elements of X. In general, finding infinite free subsets of infinite structures, requires large cardinals. We survey the field here, and examine extensions of this property due to Pereira, distilled from his work on the pcf conjecture, and recently another due to Adolf and Ben Neria. Work of the latter now establishes, with older work of the speaker, an equiconsistency between inner models with sequences of measures and their extension of  Pereira’s “Approachable Free Subset Property”.
Information: The talk will take plce in hybrid mode. Please see the seminar webpage for the link.

Barcelona Set Theory Seminar
Time: Wednesday, 4 May, 16:00-17:30 CET
Speaker: Will Boney
Title: Compactness of strong logics and large cardinals
Abstract: Connections between large cardinals in set theory and
compactness principles of strong logics in model theory have a long
history, going back to Tarski (compact cardinals), Magidor,
(extendibles), and Benda (supercompacts). We discuss several
recent advances, including connecting omitting types and normal
ultrafilters; sort logic and C(n)-cardinals; abstract Henkin models and
Woodin cardinals; and virtual logic and virtual large cardinals.
Additionally, this work has connections to category theory.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 4 May, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Garrett Ervin, CMU
Title: Filter flows
Abstract: A directed hypergraph G consists of a vertex set V along with a collection of directed hyperedges (A,B), where A and B are finite subsets of V. Given a set of vertices X, we think of the edge (A,B) as being on the boundary of X if X intersects A and does not completely contain B.
We can generalize the notion of directed hypergraph as follows. A filter graph G consists of an infinite vertex set VV along with a collection of edges (F,G), where F and G are filters on VV. Given a set of vertices X, we think of the edge (F,G) as being on the boundary of X if X is F-positive and the complement of X is G-positive.
Filter graphs seem to be surprisingly graph-like. We’ll show that filter graphs satisfy the natural generalization of the max-flow/min-cut theorem, where point masses flowing along directed edges in the usual hypergraph setting are replaced by ultrafilters flowing along filter-edges.
Information: Please see the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, 6 May, 12:30pm New York time (18:30 CEST)
Speaker: James Holland, Rutgers University
Title: Weak Indestructibility and Reflection
Abstract: Assuming multiple of strong cardinals, there are lots of cardinals with small degrees of strength (i.e. κ that are κ+2-strong). We can calculate the consistency strength of these all cardinal’s small degrees of strength being weakly indestructible using forcing and core model techniques in a way similar to Apter and Sargsyan’s previous work. This yields some easy relations between indestructibility and Woodin cardinals, and also generalizes easily to supercompacts. I will give a proof sketches of these 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, 6 May, 13.30-15.00 Toronto time (19.30-21.00 CEST)
Speaker: Mirna Dzamonja, IRIF – Centre national de la recherche scientifique (CNRS) – Université deParis
Title: Morass-generic structures
Abstract: We discuss a joint work with Wiesław Kubiś on a specific way of constructing structures of size ℵ1 using finite approximations, namely by organising the approximations along a simplified morass. We demonstrate a connection with Fraïssé limits and show that the naturally obtained structure of size ℵ1 is homogeneous. Moreover, this is preserved under expansions, which leads us to a partial answer to a question of Bassi and Zucker. We give some examples of interesting structures constructed, such as the antimetric space of size ℵ1. Finally, we comment on the situation when one Cohen real is added.

# European Set Theory Conference: Deadline for Abstracts 30 April

EUROPEAN SET THEORY CONFERENCE 2022

August 29th-September 2nd, 2022
Turin, Italy

This is the second announcement concerning the ESTC2022. In particular, please notice that

• The deadline for submitting an abstract is approaching (next Saturday!): if you plan to give a contributed talk, please apply here.
• Various forms of financial support for young researchers are available. We encourage all interested students and young post-docs to apply as soon as possible.

We are looking forward to welcoming you in Turin!

Luca Motto Ros (on behalf of the organizers)

———————————————–

30/04/2022: Abstract submission for contributed talks
30/06/2022: Early registration with reduced fee
22/08/2022: Registration

MORE ON THE CONFERENCE:

The European Set Theory Conferences is a series of biannual meetings coordinated by the European Set Theory Society (ESTS). This year’s edition is organized by the Department of Mathematics of the University of Turin and ESTS, in partnership with the Clay Mathematics Institute. It is the most important conference in set theory, and gathers the worldwide leaders in the field as well as many young researchers. During the event, the prestigious Hausdorff medal will be awarded for the most influential work in set theory published in the preceding five years. There will also be a special session in honor of Boban Veličković’s 60th birthday.

Invited speakers

– Jeffrey Bergfalk (University of Vienna)
– Filippo Calderoni (University of Illinois Chicago)
– Natasha Dobrinen (University of Denver)
– Osvaldo Guzmán (Universidad Nacional Autónoma de México)
– Joel Hamkins (University of Notre Dame)
– Chris Lambie-Hanson (Czech Academy of Sciences)
– Martino Lupini (Victoria University of Wellington)
– Julien Melleray (Université de Lyon)
– Andrew Marks (University of California, Los Angeles)
– Sandra Müller (TU Wien)
– Saharon Shelah (Hebrew University of Jerusalem)
– Stevo Todorčević (University of Toronto and Centre national de la recherche scientifique)
– Jouko Väänänen (University of Helsinki)
– Zoltán Vidnyánsky (California Institute of Technology)
– Trevor Wilson (Miami University, Oxford Ohio)

Tutorials

– Yair Hayut (Hebrew University of Jerusalem)
– Grigor Sargsyan (Polish Academy of Sciences)

BobanVeličković’s 60th Birthday Celebration

– Laura Fontanella (Université Paris-Est Créteil)
– Giorgio Venturi (University of Campinas)
– Matteo Viale (University of Turin)

Scientific committee

Joan Bagaria (chair), Matthew Foreman, Moti Gitik, Péter Komjáth, Piotr Koszmider, Heike Mildenberger, Luca Motto Ros, John Steel

Local organizing committee

Alessandro Andretta, Raphaël Carroy, Luca Motto Ros, Gianluca Paolini, Francesco Parente, Salvatore Scamperti, Matteo Viale

# Online activities 25 April – 1 May

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

Leeds Models and Sets Seminar
Time: Tuesday, 26 April, 13:45-14:55 UK time (14:45-15:55 CEST)
Speaker: Tamara Servi, IMJ-PRG & Fields Institute
Title: Interdefinability and compatibility in certain o-minimal expansions of the real field
Abstract: tba
Information: Please see the seminar webpage.

KGRC Set Theory Seminar, Vienna
Time: Tuesday, 26 April, 15:00-16:30 CEST
Speaker: Miguel Moreno, Universität Wien
Title: The isomorphism relation of unsuperstable theories in the generalized Borel-reducibility hierarchy
Abstract: One of the most important questions in generalized descriptive set theory is whether there is a generalized Borel-reducibility counterpart of Shelah’s main gap theorem? (i.e. for any classifiable theory T and nonclassifiable theory T′, is the isomorphism relation of T Borel reducible to the isomorphism relation of T′?) In this talk we will study the case of unsuperstable theories. By introducing the notion of K-colorable linear orders we can construct generalized Ehrenfeucht-Mostowski models and a Borel reduction from the isomorphism relation of any classifiable theory to the isomorphism relation of any unsuperstable theory.
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

Caltech Logic Seminar
Time: Wednesday, 27 April, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Lionel Nguyen Van Thé, Aix-Marseille Université
Title: Revisiting the Erdős-Rado canonical partition theorem
Abstract: One of the numerous strengthenings of Ramsey’s theorem is due to Erdős and Rado, who analyzed what partition properties can be obtained on mm-subsets of the naturals when colorings are not necessarily finite. Large monochromatic sets may not appear in that case, but there is a finite list of behaviors, called “canonical”, to which every coloring reduces. The purpose of this talk will be to remind certain not so well-known analogous theorems of the same flavor that were obtained by Prömel in the eighties for various classes of structures (like graphs or hypergraphs), and to show how such theorems can in fact be deduced in the more general setting of Fraïssé classes.
Information: Please see the seminar webpage.

KGRC Logic Colloquium, Vienna
Time:
Thursday, 28 April, 15:00 – 15:45 CET
Speaker: Tobias Kaiser, University of Passau
Title: tba
Abstract: tba
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.

CUNY Set Theory Seminar
Time: Friday, 29 April, 12:30pm New York time (18:30 CEST)
Speaker: Andreas Blass, University of Michigan
Title: Do these ultrafilters exist, II: not Tukey top
Abstract: This is the second of two talks devoted to two properties of ultrafilters (non-principal, on omega) for which the question ‘Do such ultrafilters exist?’ is open. In this talk, I’ll discuss the property of not being at the top of the Tukey ordering (of ultrafilters on omega). I’ll start with the definition of the Tukey ordering, and I’ll give an example of an ultrafilter that is ‘Tukey top’. It’s consistent with ZFC that some ultrafilters are not Tukey top. The examples and the combinatorial characterizations involved here are remarkably similar but not identical to examples and the characterization from the previous talk. That observation suggests some conjectures, one of which I’ll disprove if there’s enough time.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 29 April, 13.30-15.00 Toronto time (19.30-21.00 CEST)
Speaker: Matteo Viale, University of Turin
Title: The (absolute) model companionship spectrum of a mathematical theory and the continuum problem
Abstract: We introduce a classification tool for mathematical theories based on Robinson’s notion of model companionship; roughly the idea is to attach to a mathematical theory T those signatures L such that T as axiomatized in L admits a(n absolute) model companion. To do so we also introduce a slight strengthening of model companionship (absolute model companionship – AMC) which characterize those model companionable L-theories T whose model companion is axiomatized by the Π2 sentences for L which are consistent with the universal theory of any L-model of T.
We use the above to analyze set theory, and we show that the above classification tools can be used to extract (surprising?) information on the continuum problem.

# Online activities 18-24 April

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

CMU Logic Seminar
Time: Tuesday, 19 April,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker:  Samson Leung, Carnegie Mellon University
Title: Categoricity results of abstract elementary classes (Part I)
Abstract: The notion of abstract elementary classes (AECs) is an axiomatic framework developed by Shelah to generalize classification theory beyond the first-order context. One central test question is the categoricity conjecture: if an AEC K is categorical in some $\mu\geq\beth_{(2^{LS(K)})^+}$, then it is categorical in all $\mu\geq\beth_{(2^{LS(K)})^+}$. After going through the axioms of AECs, we will overview some partial results in the literature, in particular those assuming tameness, type-shortness and the amalgamation property. We show that: assuming type-shortness and amalgamation over sets, the categoricity conjecture is true. Our result also provides an alternative proof to the upward categoricity transfer in first-order theories.
Information: See the seminar webpage.

CMU Set Theory Seminar
Time: Tuesday, 19 April,  4:30 – 5:45pm Pittsburgh time (22:30 – 23:45 CEST)
Speaker:  Samson Leung, Carnegie Mellon University
Title: Categoricity results of abstract elementary classes (Part II)
Abstract: We will look at the main tools used in the proof of our
categoricity transfer: good frames, multidimensional diagrams and primes.
It is known that our assumptions allow a set-theoretic argument to
transfer categoricity down to $\beth_{(2^{LS(K)})^+}$. We will discuss
examples that encode the cumulative hierarchy, which have the first
categoricity cardinals up to $\beth_{(2^{LS(K)})^+}$, but fail
amalgamation. We conjecture that a more refined set-theoretic construction
might provide such examples that also satisfy amalgamation, which will
imply the above threshold is tight.
Information: See the seminar webpage.

Caltech Logic Seminar
Time: Wednesday, 20 April, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Maciej Malicki, IMPAN
Title: Isomorphism of locally compact Polish metric structures
Abstract: The talk will be devoted to the isomorphism relations on Borel classes of locally compact Polish metric structures. Using continuous logic, one can prove that they are always Borel reducible to graph isomorphism, which implies, in particular, that isometry of locally compact Polish metric spaces is reducible to graph isomorphism. This answers a question of Gao and Kechris. As a matter of fact, locally compact Polish metric structures behave very much like countable ones. For example, Hjorth, Kechris and Louveau proved that isomorphism of countable structures that is potentially of rank α+1 multiplicative Borel class is reducible to equality on hereditarily countable sets of rank α, and the same turns out to be true about locally compact Polish metric structures. Time permitting, I will also discuss certain variants of the Hjorth-isomorphism game, recently introduced by Lupini and Panagiotopoulos.
Information: Please see the seminar webpage.

Cross-Alps Logic Seminar
Time: Friday, 22 April, 16.00-18.00 CEST
Speaker: S. Thei, University of Udine
Title: The geology of pseudo-grounds
Abstract: Four decades after the invention of forcing, Laver and independently Woodin answered one of the most natural questions regarding forcing. Is the ground model definable in its forcing extensions? Surprisingly, it turns out that the ground models of a given set-theoretic universe are uniformly definable. Fuchs, Hamkins and Reitz used this result to establish the formal foundations for set-theoretic geology that reverses the forcing construction by studying what remains from a model of set theory once the layers created by forcing are removed. Such a switch in perspective leads to another interesting question. Is the universe itself a nontrivial forcing extension of a smaller model? Reitz addressed the issue and introduced the Ground Axiom (the precursor to set-theoretic geology) which asserts that the universe is not obtained by forcing over any strictly smaller model.
This talk is about some types of inner models which are defined following the paradigm of “undoing” forcing. For example, a bedrock is a ground satisfying the Ground Axiom and the mantle is the intersection of all grounds. Once the main geological notions are in place, we will introduce inner models with the cover and approximation properties called pseudo-grounds. In particular, we will consider some generalizations of classical results to the context of class forcing and pseudo-grounds.
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, 22 April, 12:15pm New York time (18:30 CEST)
Speaker: Andreas Blass, University of Michigan
Title: Do these ultrafilters exist, I: preservation by forcing
Abstract: This is the first of two talks devoted to two properties of ultrafilters (non-principal, on omega) for which the question ‘Do such ultrafilters exist?’ is open. In this talk, I’ll discuss the property of being preserved by some forcing that adds new reals. Some forcings destroy all ultrafilters, and some (in fact many) ultrafilters are destroyed whenever new reals are added, but it is consistent with ZFC that some ultrafilters are preserved when some kinds of reals are added. I plan to prove some of these things and describe the rest. I’ll also describe a combinatorial characterization, due to Arnie Miller, of preservable ultrafilters.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 22 April, 13.30-15.00 Toronto time (19.30-21.00 CEST)
Speaker: Asger Törnquist, University of Copenhagen
Title: The mathematics of a model of the mind in psychology
Abstract: Jens Mammen, a psychologist, has proposed a model of the human mind based on the idea that the brain organizes objects in the world into two kinds of general categories: Broad categories, which he called “sense categories”, and categories of special, distinguished objects (or people), which he called “choice categories”.
From a mathematical point of view, it is interesting that Mammen formulated his model of the mind axiomatically, based on the notion of a topological space. The objects in the universe are modelled by the points in a topological space (U,S), where the (broad) sense categories are modelled by open sets in the topology S. The choice categories forms an additional collection of subsets of the universe, C, that together with the topology must adhere to certain axioms. The triple (U,S,C) is called a “Mammen space” (a term that I introduced).
Several mathematical questions arise out Mammen’s theory. For instance, if we want Mammen’s model to be able to account for all possible subsets of the universe (a property Mammen called “completeness”), then the Axiom of Choice, or at least some non-trivial consequences thereof, seem to play a role. There are also several interesting questions related to cardinal invariants, such as the “weight” of the underlying topological space of a complete Mammen space.
I will give an overview of the mathematics of Mammen spaces and known results, and also discuss the numerous unsolved problems that remain.

CUNY Set Theory Seminar
Time: Friday, 22 April, 2:00pm New York time (20:00 CEST)
Speaker: Jouko Väänänen, University of Helsinki
Title: Stationary logic and set theory
Abstract: Stationary logic was introduced in the 1970’s. It allows the quantifier ‘for almost all countable subsets s…’. Although it is undoubtedly a kind of second order logic, it is completely axiomatizable, countably compact and satisfies a kind of Downward Lowenheim-Skolem theorem. In this talk I give first a general introduction to the extension of first order logic by this ‘almost all’-quantifier. As ‘almost all’ is interpreted as ‘for a club of’, the theory of this logic is entangled with properties of stationary sets. I will give some examples of this. The main reason to focus on this logic in my talk is to use it to build an inner model of set theory. I will give a general introduction to this inner model, called C(aa), or the aa-model, and sketch a proof of CH in the model. My work on the aa-model is joint work with Juliette Kennedy and Menachem Magidor.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

# Online activities 11-17 April

Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

CMU Logic Seminar
Time: Tuesday, 12 April,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker:  Garrett Ervin, Carnegie Mellon University
Title: Flowing through networks of generalized hyperarcs
Abstract: There are many versions of the max-flow/min-cut theorem for graphs. All assert something like “the maximum flow that can travel from a set of source vertices S to a set of sinks T is equal to the minimum boundary size of a set X containing S and disjoint from T.” König’s lemma, Hall’s matching theorem, Menger’s theorem, and the max-flow/min-cut theorem itself can each be viewed as instances of this principle.
The proofs of these theorems rely crucially on the fact that the function f that measures the boundary of a given set of vertices is submodular. This means that for any finite sets of vertices X, Y we have
f(X \cap Y) + f(X \cup Y) <= f(X) + f(Y)
Here, f might measure the vertex boundary, the edge boundary, or some capacitated version of one of these.
Can the max-flow/min-cut theorem can be generalized to an arbitrary submodular function f, even one that doesn’t arise as the boundary function of a graph? At first this question seems meaningless, since the definition of a flow depends on an underlying graph. But it turns out that certain simple submodular functions can be viewed as analogues of directed arcs in a hypergraph, and sums of these functions can be viewed as networks on which flows can be defined. We show there is a class of these networks generalizing hypergraphs for which the max-flow/min-cut theorem holds.
Information: See the seminar webpage.

Singapore Logic Seminar
Time: Wednesday, 13 April, 16:00-17:00 Singapore time (10:00-11:00 CEST)
Speaker: Wang Wei
Title: Ackermann, Ramsey and Trees
Abstract: Recently, Chong, Yang and I prove that a version of Pigeonholes Principle for trees (TT1) is Π03-conservative over RCA0. So, TT1 does not imply the totality of the Ackermann function over RCA0, like the instance of Ramsey’s Theorem for 2-colorings of pairs. To fit the trend of logic talks, I am not going to present many details. Instead, I will try to recall some stories about the Ackermann function and its appearance in reverse mathematics.
Information: See the seminar webpage.

Hebrew University-Bar Ilan University – Set theory lecture series
Time: Wednesday, 13 April, 12:00-13:30 Israel Time (11:00-12:30 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the seminar announcement and zoom link.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 13 April, 14:00-16:00 Israel Time (13:00-15:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the seminar announcement and zoom link.

Caltech Logic Seminar
Time: Wednesday, 13 April, 12:00-1:00pm Pacific time (21:00-22:00 CEST)
Speaker: Jack Lutz, Iowa State
Title: Extending the Reach of the Point-to-Set Principle
Abstract: The point-to-set principle has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces RnRn. These are classical questions, meaning that their statements do not involve computation or related aspects of logic.
In this talk I will describe the extension of two algorithmic fractal dimensions — computability-theoretic versions of classical Hausdorff and packing dimensions that assign dimensions dim(x)dim⁡(x) and Dim(x)Dim⁡(x) to individual points x∈Xx∈X — to arbitrary separable metric spaces and to arbitrary gauge families. I will then discuss the extension of the point-to-set principle to arbitrary separable metric spaces and to a large class of gauge families. Finally, I will indicate how the extended point-to-set principle can be used to prove new theorems about classical fractal dimensions in hyperspaces.
This is joint work with Neil Lutz and Elvira Mayordomo.
Information: Please see the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, 15 April, 12:15pm New York time (18:15 CEST)
Speaker: Joel David Hamkins, Notre Dame University
Title: The surprising strength of reflection in second-order set theory with abundant urelements
Abstract: I shall give a general introduction to urelement set theory and the role of the second-order reflection principle in second-order urelement set theory GBCU and KMU. With the abundant atom axiom, asserting that the class of urelements greatly exceeds the class of pure sets, the second-order reflection principle implies the existence of a supercompact cardinal in an interpreted model of ZFC. The proof uses a reflection characterization of supercompactness: a cardinal κ is supercompact if and only if for every second-order sentence ψ true in some structure M (of any size) in a language of size less than κ is also true in a first-order elementary substructure m≺M of size less than κ. This is joint work with Bokai Yao.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.