Boise Extravaganza in Set Theory 2021

BEST begins next Thursday, 17 June. We are looking forward to seeing you! The latest information will always be available on the website:  https://www.boisestate.edu/math/best/

Sam Coskey
On behalf of the organizers

Plenary speakers

• David Fernández Bretón (UNAM). Hindman’s theorem as a weak version of the Axiom of Choice
• Victoria Gitman (CUNY). Characterizing large cardinals via abstract logics
• Jun Le Goh (Wisconsin). Inseparable pairs and recursion theory
• Lynne Yengulalp (Wake Forest). Completeness, G-deltas, and games
• Joseph Zielinski (North Texas). Orbit equivalence relations of some classes of non-locally compact Polish groups

• Filippo Calderoni (UIC). Rotation equivalence and cocycle superrigidity for compact actions
• Natasha Dobrinen (Denver). Big Ramsey degrees of universal inverse limit structures
• Thomas Gilton (Pittsburgh). Club stationary reflection and the special Aronszajn tree property
• Osvaldo Guzmán González (UNAM). MAD families and strategically bounding forcings
• Randall Holmes (Boise). An outline of a proof of the consistency of New Foundations
• Martina Iannella (Udine). The complexity of convex bi-embeddability among countable linear orders
• Krzysztof Kowitz (Gdańsk). Differentially compact space and Hindman space
• Maxwell Levine (Freiburg). Patterns of stationary reflection
• Renan Mezabarba (UFES). A characterization of productive cellularity
• Aristotelis Panagiotopoulos (Münster). Dynamical obstructions to classification by (co)homology and other TSI-group invariants
• Nick Ramsey (UCLA). Exact saturation in pseudo-elementary classes
• Panagiotis Rouvelas (Patras). Models of predicative NF
• Cory Switzer (KGRC). Tight eventually different families
• Riley Thornton (UCLA). Effectivization in Borel combinatorics
• Kameryn Williams (Hawaii). Coding sets into inner mantles
• Jenna Zomback (UIUC). Ergodic theorems along trees

Online Activities 14 – 20 June

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 14 June, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: László Márton Tóth, EPFL
Title: Schreier decorations of unimodular random graphs
Abstract: It is a nice exercise in combinatorics to show that every 2d2d-regular finite graph arises as a Schreier graph of the free group FdFd. I will present generalizations of this fact to a measurable setting, as well as some examples showing the limitations. I will formulate these results using both the language of unimodular random networks and that of (p.m.p.) graphings, which are two sides of the same coin. Partially joint work with Ferenc Bencs and Aranka Hrušková.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 16 June, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Tzoor Plotinkov
Title: The Automorphism Tower of a Group
Abstract: We will talk about the operation of forming the automorphism tower over a certain group. Namely, looking at the automorphism group of a certain group, on the automorphism group of that group, and so forth, continuing transfinitely.In the late 80’s Simon Thomas showed that for every centerless group , the automorphism tower of  stabilizes in fewer than  many steps.The question of when the tower stabilizes has been studied by Thomas, Shelah, Just, Hamkins, Fuchs, Lucke and more, and turned out to have a lot of set theoretical content. We will have two talks going over some of the proofs and techniques used in the subject. The first one will be more dedicated to outright ZFC results, and the second one will be more focused on consistency results.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time:
Wednesday, 16 June, 16:30-18:00 UK time (17:30-19:00 CEST)
Speaker: Joan Bagaria, University of Barcelona
Title: Some recent results on Structural Reflection
Abstract: The general Structural Reflection (SR) principle asserts that for every definable, in the first-order language of set theory, possibly with parameters, class C of relational structures of the same type there exists an ordinal 𝛼α that reflects C, i.e.,  for every 𝐴A in C there exists 𝐵B in ∩𝑉𝛼C∩Vα and an elementary embedding from 𝐵B into 𝐴A. In this form, SR is equivalent to Vopenka’s Principle (VP). In my talk I will present some different natural variants of SR which are equivalent to the existence some well-known large cardinals weaker than VP. I will also consider some forms of SR, reminiscent of Chang’s Conjecture, which imply the existence of large cardinal principles stronger than VP, at the level of rank-into-rank embeddings and beyond. The latter is a joint work with Philipp Lücke.

KGRC Research Seminar, Vienna
Time:
Thursday, 17 June , 15:00-16:30 CET
Speaker: David Chodounský, Czech Academy of Sciences
Title: Big Ramsey degrees of 3-uniform hypergraphs are finite
Abstract: It is well known that the (universal countable) Rado graph has finite big Ramsey degrees. I.e., given a finite colouring of n-tuples of its vertices there is a copy of the Rado graph such that its n‑tuples have at most D(n)‑many colours. The proof of this fact uses a theorem of Milliken for trees, I will give sketch of the argument. I will moreover sketch an extension of the proof which works also for universal structures with higher arities, in particular 3‑uniform hypergraphs.
Joint work with M. Balko, J. Hubička, M. Konečný, and L. Vena, see https://arxiv.org/abs/2008.00268.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 18 June, 16:30-18:30 CET
Speaker: C. Brech, Universidade de São Paulo
Title: tba
Abstract: tba
Information: Online on WebEx. Please see the seminar webpage.

Online Activities 7 – 13 June

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 7 June, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Julien Melleray, Université Lyon 1
Title: A new proof of a theorem of Giordano, Putnam, and Skau
Abstract: A well-known result of Giordano-Putnam-Skau asserts that two minimal homeomorphisms of the Cantor space which have the same invariant Borel probability measures are orbit equivalent. I will present a new, rather elementary, proof of that fact, based on a strengthening of a 1979 theorem of Krieger concerning minimal actions of certain locally finite groups on the Cantor space. No familarity with topological dynamics will be assumed.
This is joint work with Simon Robert (Lyon).
Information: Check on the seminar webpage if the seminar will take place.

Time: Wednesday, 9 June, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 9 June, 15:15-16:45 CET
Speaker: Gunter Fuchs, CUNY)
Title: Fragments of (diagonal) strong reflection
Abstract: Continuation of last week’s talk.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 9 June, 16:00-17:30 CET
Speaker: Raffaella Cutolo, Università degli Studi di Napoli Federico II
Title: N-Berkeley cardinals and the two futures of set theory
Abstract: The talk will focus on Berkeley cardinals – the strongest known large
cardinal axioms – and their relativized version to inner models of ZFC, which
in fact play a decisive role in the current scenario of set theory. As we shall
see, by recent results of Woodin, there are just two, opposite possible futures
for set theory, and Berkeley cardinals are very involved in the question of
which of the two futures will prevail. In particular, the relativized version of
Berkeley cardinals turns out to be relevant with respect to that question, and
it is therefore worthy of attention.
We shall show the first example of the existence of a “N-Berkeley cardinal”
for an inner model N of ZFC, a result that is quite surprising as the involved
model N is a weak extender model, that is, N satisfies structural properties
making it very close to the set-theoretic universe V with respect to the large
cardinal axioms it is able to recognize; nevertheless, there exists (in V ) a
N-Berkeley cardinal, one that cannot exist in N, which models AC. We then
isolate a strong version of the notion of being N-Berkeley, and prove that
such strong version is inconsistent with the assumption that N is closed under
ω-sequences.
We finally illustrate the relevance of the results above with respect to the
crucial decision between the two futures of set theory.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Turin-Udine logic seminar
Time: Friday, 11 June, 16:30-18:30 CET
Speaker: Victoria Gitman, CUNY Graduate Center
Title: The old and the new of virtual large cardinals
Abstract: The idea of defining a generic version of a large cardinal by asking that some form of the elementary embeddings characterizing the large cardinal exist in a forcing extension has a long history. A large cardinal (typically measurable or stronger) can give rise to several natural generic versions with vastly different properties. For a \emph{generic large cardinal}, a forcing extension should have an elementary embedding j:V→Mof the form characterizing the large cardinal where the target model M is an inner model of the forcing extension, not necessarily contained in V. The closure properties on Mmust correspondingly be taken with respect to the forcing extension. Very small cardinals such as ω1 can be generic large cardinals under this definition. Quite recently set theorists started studying a different version of generic-type large cardinals, called \emph{virtual large cardinals}. Large cardinals characterized by the existence of an elementary embedding j:V→M typically have equivalent characterizations in terms of the existence of set-sized embeddings of the form j:Vλ→M. For a virtual large cardinal, a forcing should have an elementary embedding j:Vλ→M of the form characterizing the large cardinal with M∈Vand all closure properties on M considered from V’s standpoint. Virtual large cardinals are actually large cardinals, they are completely ineffable and more, but usually bounded above by an ω-Erd\H os cardinal. Despite sitting much lower in the large cardinal hierarchy, they mimic the reflecting properties of their original counterparts. Several of these notions arose naturally out of equiconsistency results. In this talk, I will give an overview of the virtual large cardinal hierarchy including some surprising recent directions.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 11 June, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

Online Activities 31 May – 6 June

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 2 June, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 2 June, 15:15-16:45 CET
Speaker: Gunter Fuchs, CUNY
Title: Fragments of (diagonal) strong reflection.
Abstract: I will talk about reflection principles that arose out of an attempt to find an analog of Todorcevic’s strong reflection principle SRP, which captures many of the major consequences of Martin’s Maximum, that works with forcing axioms for other forcing classes, in particular subcomplete forcing. Since SRP fails to encapsulate phenomena of diagonal reflection which follow from MM, I will propose a diagonal version of it that does have these consequences, as well as its fragments. The gist of these principles is that there is a natural strengthening of the concept of a projective stationary set, which I call “spread out”, which gives rise to the subcomplete fragments of these strong reflection principles. Part of this work is joint with Sean Cox.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 2 June, 16:00-17:30 CET
Speaker: Michał Godziszewski
Title: The Multiverse, Recursive Saturation and Well-Foundedness Mirage
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 is a countable omega-nonstandard
model of ZFC, 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 omega-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 satisfies ‘M is omega-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. We give two different versions of the Well-Foundedness Mirage axiom — what we call Weak Well-Foundedness Mirage (saying that if M is a model in the Multiverse then there is a model N in the Multiverse such that M is an element of N and N satisfies ‘M is nonstandard’ and Covering Well-Foundedness Mirage (saying that if M is a model in the Multiverse then there is a model N in the Multiverse with K in N such that K is an end-extension of M and N satisfies ‘K is omega-nonstandard.’ I will try to present constructions of two different Multiverses satisfying these two weakened axioms (with a promise concerning at least one of them, with the second one depending on what time permits). This is joint work with V. Gitman. T. Meadows and K. Williams.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time:
Wednesday, 2 June, 16:30-18:00 UK time (17:30-19:00 CEST)
Speaker: Christopher Turner, Bristol
Title: Forcing Axioms and Name Principles
Abstract: Forcing axioms are a well-known way of expressing the concept ”there are filters in V which are close to being generic”. \textit{Name principles} are another expression of this concept. A name principle says: ”Let $\sigma$ be any sufficiently nice name which is forced to have some property. Then there is a filter $g\in V$ such that $\sigma^g$ has that property.” Name principles have often been used on an ad-hoc basis in proofs, but have not been studied much as axioms in their own right. In this talk, I will present some of the connections between different name principles, and between name principles and forcing axioms. This is based on joint work with Philipp Schlicht.

Turin-Udine logic seminar
Time: Friday, 4 June, 16:30-18:30 CET
Speaker: M. Pinsker, Vienna University of Technology
Title: tba
Abstract: tba
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 4 June, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 4 June, 2pm New York time (20:00 CET)
Speaker: Gabriel Goldberg, University of Berkeley
Title: The HOD conjecture and the structure of elementary embeddings: Part II
Abstract: Woodin’s HOD conjecture asserts that in the context of very large cardinals, the inner model HOD closely approximates the universe of sets in the same way Gödel’s constructible universe does assuming 0# does not exist. The subject of these two talks is the relationship between Woodin’s conjecture and certain constraints on the structure of elementary embeddings of the universe of sets. For example, in the second talk, we will prove that any two elementary embeddings of the universe of sets into the same inner model agree on HOD, while if a local version of this theorem held, then the HOD conjecture would follow.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 24-30 May

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 24 May, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Spencer Unger, University of Toronto
Title: Borel factor maps and embeddings between actions of Zd
Abstract: We are interested in generalizations of some theorems of ergodic theory to the Borel context, particularly for natural spaces of tilings, colorings and Hamilton paths. The work combines dynamical properties of actions of ZdZd with the finite combinatorics of the ZdZd lattice. This is joint work with Nishant Chandgotia.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 26 May, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Menachem Magidor
Title: When  complicated relation on a Polish space can be Borel
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 26 May, 16:00-17:30 CET
Speaker: David Aspero, Norwich
Title: Around (*)
Abstract: Abstract: In this talk I will present work motivated by the derivation of the
Pmax axiom (*) from Martin’s Maximum++.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time:
Wednesday, 26 May, 16:30-18:00 UK time (17:30-19:00 CEST)
Speaker: Sandra Müller, University of Vienna
Title: The strength of determinacy when all sets are universally Baire
Abstract: The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson showed that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.

KGRC Research Seminar, Vienna
Time:
Thursday, 27 May, 15:00-16:30 CET
Speaker: Diana Carolina Montoya (KGRC)
Title: Independent families and singular cardinals
Abstract: In this talk, we will discuss the concept of independent families for uncountable cardinals. First, we will mention a summary of results regarding the existence of such families in the case of an uncountable regular cardinal. In the second part, we focus on the singular case and present two results of ours. This is joint work with Omer Ben-Neria.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 28 May, 16:30-18:30 CET
Speaker: D. Bartosova, University of Florida
Title: Short exact sequences and universal minimal flows
Abstract: We will investigate an interplay between short exact sequences of topological groups and their universal minimal flows in case one of the factors is compact. We will discuss possible and impossible extensions of the results in a few directions. An indispensable ingredient in our technique is a description of the universal pointed flow of a given group in terms of filters on the group, which we will describe.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 28 May, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 28 May, 2pm New York time (20:00 CET)
Speaker: Gabriel Goldberg, University of Berkeley
Title: The HOD conjecture and the structure of elementary embeddings
Abstract: Woodin’s HOD conjecture asserts that in the context of very large cardinals, the inner model HOD closely approximates the universe of sets in the same way Gödel’s constructible universe does assuming 0# does not exist. The subject of these two talks is the relationship between Woodin’s conjecture and certain constraints on the structure of elementary embeddings of the universe of sets. For example, in the second talk, we will prove that any two elementary embeddings of the universe of sets into the same inner model agree on HOD, while if a local version of this theorem held, then the HOD conjecture would follow.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 17-23 May

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 17 May, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Robin Tucker-Drob, Texas A&M
Title: Orbit equivalence and wreath products
Abstract: Let FF be a nonabelian free group. We show that, for any two nontrivial finite groups, the natural actions of the wreath product groups A≀FA≀F and B≀FB≀F, on AFAF and BFBFrespectively, are orbit equivalent. On the other hand, we show that these actions are not even stably orbit equivalent if FF is replaced with any ICC sofic group with property (T), and AA and BB have different cardinalities. This is joint work with Konrad Wrobel.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 19 May, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Menachem Magidor
Title: When  complicated relation on a Polish space can be Borel
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 19 May, 15:15-16:45 CET
Speaker:  Azul Fatalini
Title: Forcing a Mazurkiewicz set.
Abstract:  A subset of the plane is called a Mazurkiewicz set iff its intersection with every line is exactly two points. There is a well-known construction of these sets in ZFC, using transfinite recursion of the length of the continuum. We will talk about the construction of a model of ZF+DC with no well-ordering of the reals that has a Mazurkiewicz set.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 19 May, 16:00-17:30 CET
Speaker: Luca Incurvati
Title: Iteration, dependence and structuralism
Abstract: In the first part of the talk, I clarify what is at stake in the debate
between accounts of the iterative conception based on the notion of
metaphysical dependence and the minimalist account I have defended in
previous work. Special attention will be paid to the relationship between
this debate and the debate between actualist and potentialist accounts of
the cumulative hierarchy. In the second part of the talk, I use the
distinctions drawn in the first part of the talk to assess an objection leveled
by Mark Gasser against structuralist accounts of mathematics.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time:
Wednesday, 19 May, 16:30-18:00 UK time (17:30-19:00 CEST)
Title: The continuous gradability of the cut-point orders of R-trees
Abstract: An R-tree is a metric space tree in which every point can be branching. Favre and Jonsson posed the following problem in 2004: can the class of orders underlying R-trees be characterised by the fact that every branch is order-isomorphic to a real interval? In the first part of the talk, I answer this question in the negative: there is a branchwise-real tree order which is not continuously gradable. In the second part, I show that a branchwise-real tree order is continuously gradable if and only if every embedded well-stratified (i.e. set-theoretic) tree is R-gradable. This tighter link with set theory is put to work in the third part answering a number of refinements of the main question, yielding several independence results.

KGRC Research Seminar, Vienna
Time:
Thursday, 20 May, 15:00-16:30 CET
Speaker: Lev Bukovsky (Pavol Jozef Šafárik University in Košice, Slovakia)
Title: Extensions of inner models of ZFC
Abstract: I would like to present some results of members of Vopěnka’s seminary in 1960’s and 1970’s (B. Balcar, P. Vopěnka, P. Hájek and me), which were either not published or published in the language of semisets theory. Consequently, those results are not commonly known.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 21 May, 16:30-18:30 CET
Speaker: L. Westrick (Penn State University)
Title: Borel combinatorics fail in HYP
Abstract: Of the principles just slightly weaker than ATR, the most well-known are the theories of hyperarithmetic analysis (THA). By definition, such principles hold in HYP. Motivated by the question of whether the Borel Dual Ramsey Theorem is a THA, we consider several theorems involving Borel sets and ask whether they hold in HYP. To make sense of Borel sets without ATR, we formalize the theorems using completely determined Borel sets. We characterize the completely determined Borel subsets of HYP as precisely the sets of reals which are Delta^1_1 in L_{\omega_1^{ck}}. Using this, we show that in HYP, Borel sets behave quite differently than in reality. In HYP, the Borel dual Ramsey theorem fails, every n-regular Borel acyclic graph has a Borel 2-coloring, and the prisoners have a Borel winning strategy in the infinite prisoner hat game. Thus the negations of these statements are not THA. Joint work with Henry Towsner and Rose Weisshaar.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 21 May, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 21 May, 1pm New York time (19:00 CET)
Speaker: Omer Ben-Neria, Hebrew University
Title: Mathias-type Criterion for the Magidor Iteration of Prikry forcings
Abstract: In his seminal work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals known as the Magidor iteration. The purpose of this talk is to present a Mathias-type criterion which characterizes when a sequence of omega-sequences is generic for the Magidor iteration. The result extends a theorem of Fuchs, who introduced a Mathias criterion for discrete products of Prikry forcings. We will present the new criterion, discuss several applications, and outline the main ideas of the proof.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 10-16 May

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 10 May, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Luca Motto Ros, University of Turin
Title: Arcs, knots, and convex embeddability
Abstract: Working in the framework of Borel reducibility, we analyze the complexity of the natural counterparts in terms of quasi-orders of the well-known relations of equivalence for arcs and knots. It turns out that this problem is related to the study of convex embeddability between countable linear orders (and of its analogue for circular orders), which is a topic of independent interest. This is work in progress, joint with Iannella, Kulikov and Marcone.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 12 May, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Menachem Magidor
Title: When  complicated relation on a Polish space can be Borel
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 12 May, 15:15-16:45 CET
Speaker:  Jindrich Zapletal, University of Florida
Title: Chromatic numbers of distance graphs on Euclidean spaces
Abstract: Let Gn be the graph on n-dimensional Euclidean space connecting points of rational distance. I will show that it is consistent relative to an inaccessible cardinal that ZF+DC holds, chromatic number of G3 is countable, yet the chromatic number of G4 is uncountable. I will use the opportunity to explain the basic concepts,methods, and results of geometric set theory, as contained in a recent book with Paul Larson.
In the first lecture, I will provide a broad outline of geometric set theory. I will define balanced forcing, a class of partial orders which can be used to prove numerous independence results in ZF+DC, and prove its central theorems. In its usage and flexibility, balanced forcing is a parallel to proper forcing in the context of choiceless set theory. In the second lecture, I will discuss chromatic numbers of algebraic hypergraphs in general and the rational distance graphs in particular. Finally, I will construct a coloring poset which yields the consistency result mentioned in the first paragraph.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 12 May, 16:00-17:30 CET
Speaker: Sakae Fuchino
Title: Generically supercompact cardinals as reflection principles
Abstract: Bernhard König proved in his 2004 paper that the assertion omega_2 is
generically supercompact by sigma-closed forcing” is equivalent to his “Strong
Game Reflection Principle”.
We consider a generalization of this result and discuss about the relationship of
generic supercompactness of omega_2 and the existence of a Laver-generically
supercompact cardinal. The talk is connected with the on-going research
programme of the speaker together with Hiroshi Sakai which was started with
[1] Sakaé Fuchino, André Ottenbreit Maschio Rodrigues, and Hiroshi
Sakai. Strong downward Löwenheim-Skolem theorems for stationary logics I,
Archive for Mathematical Logic, Vol.60, 1-2, (2021), 17–47.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Turin-Udine logic seminar
Time: Friday, 14 May, 16:30-18:30 CET
Speaker: R. Sklinos, Stevens Institute of Technology
Title: Fields interpretable in the free group
Abstract: After Sela and Kharlampovich-Myasnikov proved that nonabelian free groups share the same common theory, a model theoretic interest for the theory of the free group arose. Moreover, maybe surprisingly, Sela proved that this common theory is stable. Stability is the first dividing line in Shelah’s classification theory and it is equivalent to the existence of a nicely behaved independence relation – forking independence. This relation, in the theory of the free group, has been proved (Ould Houcine-Tent and Sklinos) to be as complicated as possible (n-ample for all n). This behavior of forking independence is usually witnessed by the existence of an infinite field. We prove that no infinite field is interpretable in the theory of the free group, giving the first example of a stable group which is ample but does not interpret an infinite field.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 14 May, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 14 May, 2pm New York time (20:00 CET)
Speaker: Corey Switzer, University of Vienna
Title: Tight Maximal Eventually Different Families
Abstract: Maximal almost disjoint (MAD) families and their relatives have been an important area of combinatorial and descriptive set theory since at least the 60s. In this talk I will discuss some relatives of MAD families, focussing on eventually different families of functions f:ω→ω and eventually different sets of permutations p∈S(ω). In the context of MAD families it has been fruitful to consider various strengthenings of the maximality condition to obtain several flavors of ‘strongly’ MAD families. One such strengthening that has proved useful in recent literature is that of tightness. Tight MAD families are Cohen indestructible and come with a properness preservation theorem making them nice to work with in iterated forcing contexts.
I will introduce a version of tightness for maximal eventually different families of functions f:ω→ω and maximal eventually different families of permutations p∈S(ω) respectively. These tight eventually different families share a lot of the nice, forcing theoretic properties of tight MAD families. Using them, I will construct explicit witnesses to ae=ap=ℵ1 in many known models of set theory where this equality was either not known or only known by less constructive means. Working over L we can moreover have the witnesses be Π11 which is optimal for objects of size ℵ1 in models where CH fails. These results simultaneously strengthen several known results on the existence of definable maximal sets of reals which are indestructible for various definable forcing notions. This is joint work with Vera Fischer.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 26 April – 2 May

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 26 April, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Noé de Rancourt, University of Vienna
Title: A dichotomy for countable unions of smooth Borel equivalence relations
Abstract: I will present a dichotomy for equivalence relations on Polish spaces that can be expressed as countable unions of smooth Borel subequivalence relations. It can be seen as an extension of Kechris-Louveau’s dichotomy for hypersmooth Borel equivalence relations. A generalization of our dichotomy, for equivalence relations that can be expressed as countable unions of Borel equivalence relations belonging to certain fixed classes, will also be presented. This is a joint work with Benjamin Miller.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 28 April, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Menachem Magidor
Title: When is a nice complicated equivalence relation Borel some where
Abstract: The original problem is due to  Kanovei, Sabok and Zapletal: Given an analytic equivalence relation , which is not Borel. Can we find a non trivial Borel set , such that the restriction of the relation to it  is Borel.
‘Non trivial”  here means positive with respect to some sigma-complete ideal on the Borel algebra It turns out that in order to avoid simple counter example we have to make some assumptions about the equivalence relation and about the ideal.There are some results due (independently) to Chan and Drucker, about this problem assuming some large cardinals.
We shall survey some of these results and discuss the issue of trying to generalize these results to larger family of equivalence relations (e.g. Universally Baire)-These are joint results with W. Chan.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 28 April, 15:15-16:45 CET
Speaker: Farmer Schlutzenberg
Title: Local mantles of L[x]
Abstract: Recall that for a cardinal κ, a <κ-ground is an inner model W of ZFC such that V is a set-generic extension of W, as witnessed by a forcing of size <κ, and the κ-mantle is the intersection of all <κ-grounds. We will start with a brief overview
of some known facts on the κ-mantle. Following this, assuming sufficient large cardinals, we will analyze the κ-mantle M of L[x], where x is a real of sufficiently high complexity, and κ is a limit cardinal of uncountable cofinality in L[x]. We will show in particular that M models ZFC + GCH + “There is a Woodin cardinal”. We will also discuss a variant, joint with John Steel, for the κ-cc mantle, where κ is regular uncountable in L[x] and κ≤ the least Mahlo of L[x]. The proof relies on Woodin’s analysis of HODL[x,G] and Schindler’s generation of grounds, and is motivated by work of Fuchs, Sargsyan, Schindler and the author on Varsovian models and the mantle.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 28 April, 16:00-17:30 CET
Speaker: Yair Hayut
Title: omega-strongly measurable cardinals
Abstract: In his profound work towards the identification of the ultimate-L (the ultimate canonical inner model), Woodin isolated a key ingredient: the w-
strongly measurable cardinals. Those cardinals are regular in V and measurable in HOD for a very simple reason – the intersection of their club filter
with HOD splits into a small collection of isolated normal measures. Woodin’s
HOD-dichotomy implies that if one can prove that there are class many regular
cardinals which are not strongly measurable, and there exists an extendible
cardinal, then some covering theorem holds between HOD and V.
In this talk I will present a recent joint result with Omer Ben-Neria, proving the
consistency of the existence of class many strongly measurable cardinals
(indeed, all the successors of regular cardinals), from a rather mild large
cardinal hypothesis, in the realm of o(κ) = κ.
I will focus on the details of the proof for the first two cardinals À1 and À2.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

KGRC Research Seminar, Vienna
Time:
Thursday, 29 April, 15:00-16:30 CET
Speaker: Moreno Pierobon, Università di Pisa, Italy
Title: Fullness and mixing property for boolean valued models
Abstract: Besides being one of the classical approaches to forcing, boolean valued models provide a flexible tool to produce a variety of structures.
In this talk, we will investigate in details the fullness property and the mixing property for boolean valued models. The former is necessary to control the semantics when quotienting a boolean valued model by an  ultrafilter. The latter implies the former and it is easier to check.
We will show that not every model is full, and the mixing property in not equivalent to fullness. Moreover, we will improve the classical Łoś Theorem for boolean valued models.
In the end, we will give a simple characterization of the mixing property using étalé spaces. This last result is an easy corollary of a more general study we made on the categorical equivalence between boolean valued models and presheaves.
This is a joint work with Matteo Viale.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 30 April, 16:30-18:30 CET
Speaker: S. Barbina, Open University
Title: The theory of the universal-homogeneous Steiner triple system
Abstract: A Steiner triple system is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite Steiner triple systems has a Fraïssé limit, the countable homogeneous universal Steiner triple system M. In joint work with Enrique Casanovas, we have proved that the theory T of M has quantifier elimination, is not small, has TP2, NSOP1, eliminates hyperimaginaries and weakly eliminates imaginaries. In this talk I will review the construction of M, give an axiomatisation of T and prove some of its properties.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 20 April, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ingay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 30 April, 2pm New York time (20:00 CET)
Speaker: Elliot Glazer, Harvard University
Title: Paradoxes of perfectly small sets
Abstract: We define a set of real numbers to be perfectly small if it has perfectly many disjoint translates. Such sets have a strong intuitive claim to being probabilistically negligible, yet no non-trivial measure assigns them all a value of 0. We will prove from a moderate amount of choice that any total extension of Lebesgue measure concentrates on a perfectly small set, suggesting that for any such measure, translation-invariance fails ‘as badly as possible.’ From the ideas of this proof, we will also derive analogues of well-known paradoxes of randomness, specifically Freiling’s symmetry paradox and the infinite prisoner hat puzzle, in terms of perfectly small sets. Finally, we discuss how these results constrain what a paradox-free set theory can look like and some related open questions.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Postdoctoral position at the University of Bristol

There is a 30 Month Postdoctoral position available in Set Theory at the University of Bristol.

Further particulars and how to apply:https://www.bristol.ac.uk/jobs/find/details/?jobId=223715&jobTitle=Research%20Associate%20(in%20Set%20Theory)

The University of Bristol seeks outstanding candidates for a Research Associate in Set Theory, position tenable from 31st August 2021 (fixed latest start date) for a duration of maximum 30 months. The successful candidate will become a member of the Institute for Pure Mathematics within the School of Mathematics in Bristol, and will work with Philip Welch.

This research position requires the minimum expertise of a candidate with a completed PhD in Set Theory to conduct investigations in problems associated with Welch’s EPSRC funded research grant Graphs on Generalized Baire Spaces.  There has been a surge of interest in recent years on extending the descriptive set theory of Baire space to spaces of the form kappa^kappa for kappa a regular cardinal. The main focus of the project is on the interaction of descriptive set theoretic notions at this analogous level, Inner Model Theory, infinitary game theoretic methods and forcing axioms. Accordingly candidates will be expected to have particular expertise in one or more of these areas.

We welcome applications from all members of our community and are particularly encouraging those from diverse groups, such as members of the LGBT+ and BAME communities, to join us.

Please note that it is the applicant’s responsibility to ensure their referees send a letter of reference by email to maths-recruitment@bristol.ac.uk before the advert closes and please can we ask you add the vacancy reference number in the email title.

Online Activities 19-25 April

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 19 April, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Francois Le Maitre, University of Paris
Title: A characterization of high transitivity for groups acting on trees
Abstract: A countable group is highly transitive if it admits an embedding in the permutation group of the integers with dense image. I will present a joint work with Pierre Fima, Soyoung Moon and Yves Stalder where we show that a large class of groups acting on trees are highly transitive, which yields a characterization of high transitivity for groups admitting a minimal faithful action of general type on a tree thanks to the work of Le Boudec and Matte Bon. Our proof is new even for the free group on two generators and I will give a detailed overview in this very particular case, showing that the generic transitive action of the free group on two generators is highly transitive.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 21 April, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Omer Ben Neria
Title: Strong Prikry property for Magidor Iterations
Abstract: In his celebrated work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals, known as the Magidor iteration.The purpose of this talk is to state and prove a version of the strong Prikry Lemma for such iterations, extending a result of Fuchs for the case where the set of measurables is discrete.  We will also describe several applications regarding the genericity of sequences of critical points in iterated ultrapowers.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 21 April, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 21 April, 16:00-17:30 CET
Speaker: Sam Roberts
Title: Reinhardt’s potentialism
Abstract: Reflection principles have been of interest to philosophers and mathematicians because they promise to be well-motivated additions to the standard axioms of set theory that nonetheless settle many of the questions left open by those axioms. Although William Reinhardt’s work on reflection principles has been immensely influential, some of his central ideas have remained unclear. The purpose of my talk will be to rectify this. I will start by outlining and formalising his primary contribution to the literature on reflection principles, which is a version of potentialism. I will then show that it is remarkably strong and discuss a number of criticisms.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

KGRC Research Seminar, Vienna
Time:
Thursday, 22 April, 15:00-16:30 CET
Speaker: Osvaldo Guzmán, Universidad Nacional Autónoma de México
Title: MAD families and strategically bounding forcings
Abstract: The notion of strategically bounding forcings is a natural game-theoretic strengthening of the bounding  property for partial orders.  In this talk, we will study the basic properties of strategically bounding forcings and talk about indestructibility of MAD families. The motivation for this work is the problem of Roitman.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 23 April, 16:30-18:30 CET
Speaker: F. Loregian, Tallinn University of Technology
Title: Functorial Semantics for Partial Theories
Abstract: We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of string diagrams as terms. This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational theories by considering a number of examples, including partial combinatory algebras and cartesian closed categories. Moreover, despite the increase in expressivity of the syntax we retain a well-behaved notion of semantics: we show that our categories of models are precisely locally finitely presentable categories, and that free models exist.
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 23 April, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 23 April, 2pm New York time (20:00 CET)
Speaker: Andres Villaveces, CUNY
Title: Two logics, and their connections with large cardinals / Questions for BDGM: Part II
Abstract: In the past couple of years I have been involved (joint work with Väänänen and independently with Shelah) with some logics in the vicinity of Shelah’s L1κ (a logic from 2012 that has Interpolation and a very weak notion of compactness, namely Strong Undefinability of Well-Orderings, and in some cases has a Lindström-type theorem for those two properties). Our work with Väänänen weakens the logic but keeps several properties. Our work with Shelah explores the connection with definability of AECs.
These logics seem to have additional interesting properties under the further assumption of strong compactness of a cardinal, and this brings them close to recent work of Boney, Dimopoulos, Gitman and Magidor [BDGM].
During the first lecture, I plan to describe two games and a syntax of two logics: Shelah’s L1κ and my own logic (joint work with Väänänen) L1,cκ. I will stress some of the properties of these logics, without any use of large cardinal assumptions. During the second lecture, I plan to enter rather uncharted territory. I will describe some constructions done by Shelah (mostly) under the assumption of strong compactness, but I also plan to bring these logics to a territory closer to the work of [BDGM]. This second lecture will have more conjectures, ideas, and (hopefully interesting) discussions with some of the authors of that paper.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.