Online activities 28 November – 4 December

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

Vienna Research Seminar in Set Theory
Time: Tuesday, 29 November, 15:00-16:30 CET
Speaker: Corey Switzer, Universität Wien
Title: Subversion Forcing, part 2
Abstract: In these two talks we will introduce Jensen’s classes of subcomplete and subproper forcing as well as discuss some applications due to the speaker and Fuchs, and the speaker and Sakai. An important feature of proper forcing is the countable covering property: every countable set of ordinals added by a proper forcing notion is contained in a ground model countable set of ordinals. This is important in iteration theorems. Subproper forcing is a weakening of proper forcing that is still iterable while including some well known forcing notions which do add countable sets of ordinals that are not covered by anything in the ground model including Namba forcing (under CH) and Prikry forcing. One can weaken other classes of forcing notions in a similar way and the “sub”version of the countably closed forcing, known as subcomplete forcing, is a particularly interesting subclass of subproper forcing that was used by Jensen in several applications including his solution to the extended Namba problem.
In the first of these talks I will introduce the classes subproper and subcomplete forcing as well as discuss simplifications of them due to Fuchs and myself. Time permitting I will discuss new iterations theorems for these classes reminiscent of similar theorems proved for proper forcing in the context of the reals and combinatorics on ω1 (ωω-bounding, preservation of Souslin trees etc). In the second talk I will discuss the forcing axioms for these classes including their applications and limitations. In particular, time permitting, I will discuss a recent result, joint with Hiroshi Sakai that the forcing axiom for subcomplete forcing is compatible with a □ω1-sequence. The take away is a class of strong forcing axioms that are compatible with a wide variety of behaviour on the level of the reals and combinatorics on cardinals below the continuum.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 29 November, 15:00-16:30 CET
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 29 November, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)  
Speaker:  Benjamin Siskind, Carnegie Mellon University
Title: Full normalization and HOD^L(R)
Abstract: We’ll review some aspects of the HOD analysis of L(R) and 
introduce the full normalization machinery developed by Steel and 
Schlutzenberg. We’ll use this to show that HOD^L(R)|theta is actually a 
normal iterate of M_omega|delta via M_omega’s canonical iteration strategy 
(and a bit more), a result of Steel and Schlutzenberg. Time permitting, we 
may discuss other applications of full normalization, due to Steel.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

CMU Logic Seminar
Time: Tuesday, 29 November,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)  
Speaker: Verónica Becher, University of Buenos Aires
Title: Turing’s Normal Numbers
Abstract: In a manuscript entitled “A note on normal numbers” and written 
presumably in 1937 Alan Turing gave an algorithm that produces real 
numbers normal to every integer base. This proves, for the first time, the 
existence of computable instances and provides an answer to Borel’s 
problem on giving examples of normality. Furthermore, with this work 
Turing pioneers the theory of randomness and shows that he had the 
insight, ahead of his time, that traditional mathematical concepts, like 
measure or continuity, could be made computational. In this talk I will 
highlight the ideas in these achievements of Turing, which are largely 
unknown because his manuscript remained unpublished until it appeared in 
his Collected Works in 1992.
Information: See the seminar webpage.

Helsinki Logic Seminar
Time: Wednesday, 30 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CET)
Speaker: Miika Hannula
Title: tba
Abstract: tba
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 30 November, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Thilo Weinert, University of Vienna
Title: Two New Inequalities for Cardinal Characteristics of the Continuum
Abstract: Over the last decades the theory of cardinal characteristics of the continuum has emerged as one among several important subfields of set theory. Some of the classical results in it precede the invention of forcing and arguably the aforementioned emergence. Open problems in this field have inspired the invention over ever more versatile constructions of forcing notions and much of the progress has consisted of proving the values of cardinal characteristics not to be ZFC-provably related. A recent outlier has been the celebrated result by Malliaris and Shelah that p is equal to t. I had guessed that there might be more ZFC-provable relations between the hitherto defined characteristics and I am going to talk about what I found up to now. This is to say that I am going to present some ZFC-provable inequalities. In particular I am going to show that the evasion number is at most the subseries number. These cardinal characteristics have been introduced in work by Blass, Brendle, Brian, and Hamkins and originate from Algebra and Analysis, respectively. The proof interpolates via the pair-splitting number which is due to Minami.
Information: Please see the seminar webpage.

Caltech Logic Seminar
Time: Wednesday, 30 November, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: Sumun Iyer, Cornell
Title: Dynamics of the Knaster continuum homeomorphism group
Abstract: We use the projective Fraissé approach and Ramsey’s theorem to show that the universal minimal flow of the homeomorphism group of the universal Knaster continuum is homeomorphic to the universal minimal flow of the free abelian group on countably many generators. We will define a projective Fraissé class whose limit approximates the universal Knaster continuum in such a way that the group Aut(K)Aut(K) of automorphisms of the Fraissé limit is a dense subgroup of the group, Homeo(K)Homeo(K), of homeomorphisms of the universal Knaster continuum. The computation of the universal minimal flow involves modifying the Fraissé class in a natural way so that it approximates an open, normal, extremely amenable subgroup of Homeo(K)Homeo(K).
Information: Please see the seminar webpage.

Cross-Alps Logic Seminar
Time: Friday, 2 December 16.00-18.00 CET
Speaker: F. Parente, University of Turin
Title: Good ultrafilters and universality properties of forcing
Abstract: In 1964, Keisler introduced κ-good ultrafilters, which can be characterized as those ultrafilters which produce κ-saturated ultrapowers. The problem of finding an analogous characterization for ultrafilters on Boolean algebras has been considered by Mansfield (1971), Benda (1974), and Balcar and Franek (1982), who proposed and compared different notions of “goodness” for such ultrafilters. In the first part of my talk, I shall outline the different definitions introduced in the literature and show that they are in fact all equivalent, thus providing a complete characterization of those ultrafilters which produce κ-saturated Boolean ultrapowers. In the second part of the talk, I shall present a joint work with Matteo Viale, which started in 2015 during my Master’s thesis and was recently revived during the last few months in Torino. The aim of our project is to study the universality properties of forcing. More precisely, we shall prove that, for many interesting signatures, every model of the universal theory of an initial segment of the universe can be embedded into a model constructed by forcing. To achieve this goal, we build good ultrafilters on forcing notions such as the Lévy collapsing algebra and Woodin’s stationary tower.
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, 2 December, 12:30pm New York time (18:30 CET)
Speaker: Will Boney, Texas State University
Title: tba
Abstract: tba
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 2 December, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: Eduardo Duenez, University of Texas at San Antonio, and Jose Iovino, University of Texas at San Antonio
Title: tba
Abstract: tba
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 2 December, 2:00 – 3:30 New York time (20:00-21:30 CET)
Speaker: Michał Tomasz Godziszewski, University of Vienna
Title: tba
Abstract: tba
Information: The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.

Advertisement

Online activities 21-27 November

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

Vienna Research Seminar in Set Theory
Time: Tuesday, 22 November, 15:00-16:30 CET
Speaker: Corey Switzer, Universität Wien
Title: Subversion Forcing, part 1
Abstract: In these two talks we will introduce Jensen’s classes of subcomplete and subproper forcing as well as discuss some applications due to the speaker and Fuchs, and the speaker and Sakai. An important feature of proper forcing is the countable covering property: every countable set of ordinals added by a proper forcing notion is contained in a ground model countable set of ordinals. This is important in iteration theorems. Subproper forcing is a weakening of proper forcing that is still iterable while including some well known forcing notions which do add countable sets of ordinals that are not covered by anything in the ground model including Namba forcing (under CH) and Prikry forcing. One can weaken other classes of forcing notions in a similar way and the “sub”version of the countably closed forcing, known as subcomplete forcing, is a particularly interesting subclass of subproper forcing that was used by Jensen in several applications including his solution to the extended Namba problem.
In the first of these talks I will introduce the classes subproper and subcomplete forcing as well as discuss simplifications of them due to Fuchs and myself. Time permitting I will discuss new iterations theorems for these classes reminiscent of similar theorems proved for proper forcing in the context of the reals and combinatorics on ω1 (ωω-bounding, preservation of Souslin trees etc). In the second talk I will discuss the forcing axioms for these classes including their applications and limitations. In particular, time permitting, I will discuss a recent result, joint with Hiroshi Sakai that the forcing axiom for subcomplete forcing is compatible with a □ω1-sequence. The take away is a class of strong forcing axioms that are compatible with a wide variety of behaviour on the level of the reals and combinatorics on cardinals below the continuum.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 22 November, 15:00-16:30 CET
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

Helsinki Logic Seminar
Time: Wednesday, 23 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CET)
Speaker: Balthasar Grabmayr
Title: Fixing Montague’s Problem
Abstract: Turing machines only operate directly on strings. Turing computation over any other domain therefore requires a notation system for the domain. Ever since Montague’s (1960) observation that different notation systems in general yield different notions of Turing computability, the task of distinguishing those notation systems that are admissible for computation from those that are not continues to be a much debated and open problem in the philosophy of computation. In the first part of this talk, I will introduce a generalized version of Montague’s problem. In the second part, I will formulate and defend a solution to this problem.
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 23 November, 11:00-12:00 local time (12:00-13:00 CET) – note the taim change
Speaker: Will Johnson, Fudan University
Title: Around definable types in valued fields
Abstract: Haskell, Hrushovski, and Macpherson showed that the theory ACVF of algebraically closed valued fields has elimination of imaginaries after adding the so-called “geometric sorts” to the language. The same result holds in $p$-adically closed fields ($p$CF) by work of Hrushovski, Martin, and Rideau. In the case of ACVF, one way to prove this is to encode imaginaries using definable types, and then encode definable types in the geometric sorts. While $p$CF does not have “enough” definable types to encode imaginaries, the encoding of definable types carries over. Surprisingly, the geometric sorts are unnecessary: any definable type in $p$CF has a code in the home sort (the field sort). This fact and its proof have some unexpected applications to definable groups and definable topological spaces in $p$CF. For example, certain quotient groups are definable rather than interpretable, and there is a unified notion of “definable compactness” for definable topological spaces. Parts of this talk are joint work with Pablo And\’ujar Guerrero.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 23 November, 16:00-17:30 CET
Speaker: Jiachen Yuan
Title: On the cofinality of the least omega_1-strongly compact cardinal
Abstract: In [1,2], Bagaria and Magidor introduced the notion of l-strong
compactness, which generalized the well-known notion of strong compactness. Most
surprisingly, they proved, relative to a supercompact cardinal k with a measurable d
below k, that it is consistent that the least w1-strongly compact cardinal is singular, in
contrast to the fact that strongly compact cardinals are always inaccessible. In
particular, in their model they made k be the least w1-strongly compact cardinal, which
has cofinality exactly d.
In this talk, we explore all possible cofinalities of the least w1-strongly compact
cardinal. We’ll see that it is impossible to strengthen Bagaria-Magidor’s result under
their original assumption while we are able to prove under a slightly stronger (which is
showed to be necessary) that there is no non-trivial restrictions on the cofinality.
[1] Joan Bagaria, Menachem Magidor. On w1-strongly compact cardinals, Journal of
Symbolic Logic 79, 2014
[2] Joan Bagaria, Menachem Magidor. Group radicals and strongly compact cardinals,
Trans. Amer. Math. Soc. 366, 2014, No. 4, 1857-1877.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Vienna Logic Colloquium
Time:
 Thursday, 24 November, 15:00 – 16:30 CET
Speaker: F.-V. Kuhlmann, University of Szczecin
Title: Nonstandard models of the reals and symmetrical completeness
Abstract: The notion of power series fields provides an easy method for the construction of nonstandard models of the ordered field of real numbers. I will define them, as well as Hahn products, which are their equivalent in the case of ordered abelian groups. The question arises whether these power series models can also have additional structures or properties that we know from the reals. For example, it was shown in joint work with Salma Kuhlmann and Saharon Shelah that they do not admit exponential functions which have the same elementary properties as the exponential function on the reals. In a different direction, the question came up whether they could support generalizations of Banach’s Fixed Point Theorem. I will introduce the notions of symmetrically complete ordered fields, abelian groups and sets and characterize those power series models of the reals that are symmetrically complete. They indeed admit a (nonarchimedean) generalization of Banach’s Fixed Point Theorem. Their construction is the result of joint work with Katarzyna Kuhlmann and Saharon Shelah. It heavily relies on the analysis of cuts in ordered power series fields and Hahn products.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Toronto Set Theory Seminar
Time: Friday, 25 November, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: Cesar Corral, Universidad Nacional Autónoma de México
Title: Convergence properties in the realm of Psi-spaces
Abstract: We will deal with convergence properties, mainly the Frechet-Urysohn property and some strong versions of it, as well as some properties related to the preservation of Frechetness under products, like the [\alpha_i] -properties introduced by Arhangel’skii.
We will show that these classes of spaces are (consistently) different by constructing some counterexamples making use of almost disjoint families.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

Online activities 14-20 November

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

Bristol Logic and Set Theory Seminar
Time:
 Tuesday, 15 November, 12:30-13:30 UK time (13:30-14:30 CET)
Speaker: Sam Coskey, Boise State University
Title: Jumps in the Borel complexity hierarchy
Abstract: There are several well-studied “jumps” on the class of Borel equivalence relations under Borel reducibility, which carry an equivalence relation to one of greater complexity. Examples include the jump of Friedman–Stanley and the jumps of Louveau. In joint work with John Clemens, we defined a new (ish) family of jumps called Bernoulli jumps. In this talk I will introduce and describe Bernoulli jumps, and present an application to the classification of countable scattered orders. I will conclude by summarizing some more recent developments, due to others, relating to Bernoulli jumps.
Information: The login information is posted on the seminar webpage.

Vienna Research Seminar in Set Theory
Time: Tuesday, 15 November, 15:00-16:30 CET
Speaker: Monroe Eskew, Universität Wien
Title: Compactness versus hugeness at successor cardinals, part 2
Abstract: There are several ways in which small cardinals can behave like large
ones. One variety is compactness phenomena, such as the tree property,
which characterize when inaccessible cardinals satisfy some strong large
cardinal notions, but can consistently hold at small cardinals such as
$\omega_2$. Another variety is generic embedding properties coming from
saturated ideals or Chang’s Conjecture that resemble embeddings associated
with huge cardinals. The known forcing strategies for obtaining
compactness and hugeness properties at small cardinals are very different.
Can they be made to hold simultaneously? In these talks, we present some
combinatorial barriers to combining them, and we show why several forcing
approaches will not work. Hopefully, by narrowing down the space of
possibilities, these negative results will point towards a path to
answering our question.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

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

CMU Core Model Theory Seminar
Time: Tuesday, 15 November, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)  
Speaker:  Sandra Müller, TU Wien
Title: A stationary-tower-free proof of Sealing, part 2
Abstract: Sealing is a generic absoluteness principle for the theory of
the universally Baire sets of reals introduced by Woodin. It is deeply
connected to the Inner Model Program and plays a prominent role in recent
advances in inner model theory. 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. In the first talk, 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. In the second
talk, I will outline the proof of an extension of the Sealing Theorem that
gives models in which Theta is regular. This is joint work with Grigor
Sargsyan.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

Helsinki Logic Seminar
Time: Wednesday, 16 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CET)
Speaker: Tobias Boege
Title: Incidence geometry, conditional independence and the existential theory of the reals
Abstract: Deciding whether a system of polynomial equations and inequalities has a solution over the real numbers is a basic task in computational geometry, optimization and algebraic statistics. Under polynomial-time many-one reductions, this problem generates the complexity class $\exists\mathbb{R}$. I will briefly recall a geometric technique, due to von Staudt, for obtaining completeness results for this complexity class and apply it to the implication problem for conditional independence among jointly normal random variables.
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 16 November, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Petra Staynova, University of Derby
Title: Spotting rare Pokemon
Abstract: Sometimes more abstract concepts in general topology are considered as having little relation with areas outside of topology. In this talk we will explore a beautiful construction that unexpectedly links the notion of n-Hausdorffness and a special topology in the dynamical systems setting.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 16 November, 16:00-17:30 CET
Speaker: Jeffrey Bergfalk, University of Barcelona
Title: The definable content of homological invariants
Abstract: This talk is intended as an overview of the first two installments in a series of joint works with Martino Lupini and Aristotelis Panagiotopoulos (arXiv:2210.11098, arXiv:2008.08782). The theme of this series is the recognition that many classical homological and homotopical functors from the field of algebraic topology factor through “definable categories” such as what we term the category of groups with a
Polish cover; this recognition gives rise to stronger versions of those invariants, together with closer analyses of their classifying powers. Somewhat more informally, this series is about the topological and Borel structures underlying classical invariants like the Ext or lim1 or Cech cohomology groups; although these structures had, throughout these invariants’ history, periodically been considered, what distinguishes the works under discussion is their recognition of the remarkable utility of descriptive set theoretic frameworks for systematically and efficiently doing so.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 16 November, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: Dexuan Hu, Cornell University
Title: Polish modules over subrings of Q
Abstract: We give a method of producing a Polish module over an arbitrary subring of Q from an ideal of subsets of N and a sequence in N. The method allows us to construct two Polish Q-vector spaces, U and V, such that
– both U and V embed into R, but
– U does not embed into V and V does not embed into U,
where by an embedding we understand a continuous Q-linear injection. This construction answers a question of Frisch and Shinko. In fact, our method produces a large number of incomparable with respect to embeddings Polish Q-vector spaces.
This is joint work with Slawomir Solecki.
Information: Please see the seminar webpage.

Vienna Logic Colloquium
Time:
 Thursday, 17 November, 15:00 – 16:30 CET
Speaker: F. Schlutzenberg, University of Münster
Title: The Axiom of Choice and large cardinals
Abstract: The Axiom of Choice (AC) is mostly accepted by mathematicians, and is 
essential in many proofs. However, it seems to be accepted with less 
confidence than the other axioms of set theory, probably due to its 
non-constructive nature and its various unexpected consequences. Large 
cardinals are central axioms in set theory, with compelling consequences 
for the universe of sets, not only for “large” sets but also for “small” 
ones like real numbers and sets thereof. It turns out that the 
relationship between AC and large cardinals is intricate, and not entirely 
without conflict. The connections might even be taken to suggest that the 
correct picture of the universe of sets is one in which very large 
cardinals exist and the full Axiom of Choice must fail. I will survey some 
of the recent work in this area. The talk will be aimed at a general logic 
audience.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 18 November 16.00-18.00 CET
Speaker: A. Conversano, Massey University
Title: Tools of o-minimality in the study of groups
Abstract: In this talk we will see how geometric invariants of definable sets in o-minimal structures can be used to understand the structure of groups in several categories.
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, 18 November, 12:30pm New York time (18:30 CET)
Speaker: Brent Cody, Virginia Commonwealth University
Title: Sparse analytic systems
Abstract: Given a set S, an S-predictor P is a function that takes as inputs functions of the form f:(−∞,t)→S, where t∈R, and outputs a guess P(f) for what f(t) ‘should be.’ An S-predictor is good if for all total functions F:R→S the set of t∈R for which the guess P(F↾(−∞,t)) is not equal to F(t) has measure zero. Hardin and Taylor proved that every set S has a good S-predictor and they raised various questions asking about the extent to which the prediction P(f) made by a good predictor might be invariant after precomposing f with various well-behaved functions – this leads to the notion of ‘anonymity’ of good predictors under various classes of functions. Bajpai and Velleman answered several of Hardin and Taylor’s questions and asked: Does there exist, for every set S, a good S-predictor that is anonymous with respect to the strictly increasing analytic homeomorphisms of R? We provide a consistently negative answer to this question by strengthening a result of Erdős, which states that the Continuum Hypothesis is equivalent to the existence of an uncountable family F of (real or complex) analytic functions, such that {f(x):f∈F} is countable for every x. We strengthen Erdős’ result by proving that CH is equivalent to the existence of what we call sparse analytic systems of functions. This is joint work with Sean Cox and Kayla Lee.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 18 November, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: Nishant Chandgotia, TIFR
Title: About Borel and almost Borel embeddings for Zd actions
Abstract: How can you code a system? This question has many perspectives depending on what we mean by code and by system. In this talk we will take the perspective of an ergodic theorist and look at encoding of free ergodic probability preserving transformations. A classical result here is due to Krieger who showed that this encoding can be done by bi-infinite sequence of unconstrained symbols from a finite alphabet. In this talk we will be talking about analogous theorems for encodings of Zd actions when these symbols have constraints (for instance when adjacent symbols are distinct or systems arising from tilings) which use some interesting combinatorial estimates of independent interest.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 18 November, 2:00 – 3:30 New York time (20:00-21:30 CET)
Speaker: Dima Sinapova, Rutgers University
Title: Prikry sequences and square properties at ℵω
Abstract: It is well known that if an inaccessible cardinal κ is singularized to countable cofinality while preserving cardinals, then □κω holds in the outer model. Moreover, this remains true even when relaxing the cardinal preservation assumption a bit. In this talk we focus on when Prikry forcing adds weaker forms of square in a more general setting. We prove abstract theorems about when Prikry forcing with interleaved collapses to bring down the singularized cardinal to ℵω will add a weak square sequence. This can be viewed as a partial positive result to a question of Woodin about whether the failure of SCH at ℵω implies weak square.
Information: The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.

Online activities 7-13 November

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

Vienna Research Seminar in Set Theory
Time: Tuesday, 8 November, 15:00-16:30 CET
Speaker: Monroe Eskew, Universität Wien
Title: Compactness versus hugeness at successor cardinals, part 1
Abstract: There are several ways in which small cardinals can behave like large
ones. One variety is compactness phenomena, such as the tree property,
which characterize when inaccessible cardinals satisfy some strong large
cardinal notions, but can consistently hold at small cardinals such as
$\omega_2$. Another variety is generic embedding properties coming from
saturated ideals or Chang’s Conjecture that resemble embeddings associated
with huge cardinals. The known forcing strategies for obtaining
compactness and hugeness properties at small cardinals are very different.
Can they be made to hold simultaneously? In these talks, we present some
combinatorial barriers to combining them, and we show why several forcing
approaches will not work. Hopefully, by narrowing down the space of
possibilities, these negative results will point towards a path to
answering our question.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 8 November, 15:00-16:30 CET
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 8 November, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)  
Speaker:  Sandra Müller, TU Wien
Title: A stationary-tower-free proof of Sealing, part 1
Abstract: Sealing is a generic absoluteness principle for the theory of
the universally Baire sets of reals introduced by Woodin. It is deeply
connected to the Inner Model Program and plays a prominent role in recent
advances in inner model theory. 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. In the first talk, 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. In the second
talk, I will outline the proof of an extension of the Sealing Theorem that
gives models in which Theta is regular. This is joint work with Grigor
Sargsyan.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

CMU Logic Seminar
Time: Tuesday, 8 November,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)  
Speaker: Harrison-Trainor, University of Michigan
Title: Computable Approximations and True Stages
Abstract: The limit lemma says that a set is computable relative to the Halting problem if it can be approximated computably with finitely many mind changes. More complicated sets can also be approximated with more complicated approximation schemes, but these quickly become unwieldy. Many frameworks have been proposed for dealing with these approximations, such the $alpha$-systems of Ash and Knight or the true stages of Montalban. In the first half of the talk, I’ll describe the general ideas of some of these frameworks and some of their applications. In the second half of the talk, I will talk about a new framework of true stages (with Adam Day, Noam Greenberg, and Dan Turetsky) with connections to descriptive set theory. This framework can be thought of as a computability-theoretic change-of-topology with additional bonuses.
Information: See the seminar webpage.

Helsinki Logic Seminar
Time: Wednesday, 9 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CET)
Speaker: Vadim Weinstein
Title: tba
Abstract: tba
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 9 November, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Mariana Vicaria, UCLA
Title: Elimination of imaginaries in ordered abelian groups of bounded regular rank
Abstract: In this talk I will present some results about elimination of imaginaries in pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries once we add sorts for the quotient groups $\Gamma/ \Delta$ for each definable convex subgroup $\Delta$, and sorts for the quotient groups $\Gamma/(\Delta+ \ell\Gamma)$ where $\Delta$ is a definable convex subgroup and $\ell \in \mathbb{N}{\geq 2}$. We refer to these sorts as the \emph{quotient sorts}. For the dp-minimal case we obtain a complete elimination of imaginaries if we also add constants to distinguish the cosets of $\Delta+\ell\Gamma$ in $\Gamma$, where $\Delta$ is a definable convex subgroup and $\ell \in \mathbb{N}{\geq 2}$.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 9 November, 16:00-17:30 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 9 November, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: Simon Thomas, Rutgers University
Title: Some Open Problems On Invariant Random Subgroups
Abstract: Let G be a countably infinite group and let SubG be the compact space of subgroups H⩽G. Then an invariant random subgroup (IRS) of G is a probability measure ν on SubG which is invariant under the conjugation action of G on SubG.
In this talk, after a brief introduction to the theory of invariant random subgroups, I will discuss some of the many basic questions in this relatively new area. For example, if ν is an ergodic IRS of a countable group G, then we obtain a corresponding zero-one law on SubG for the class of group-theoretic properties Φ such that the set {H∈SubG∣H has property Φ} is ν-measurable; and thus ν concentrates on a collection of subgroups which are quite difficult to distinguish between. Consequently, it is natural to ask whether there exists an ergodic IRS of a countable group G which does not concentrate on the subgroups H⩽G of a single isomorphism type.
Information: Please see the seminar webpage.

Vienna Logic Colloquium
Time:
 Thursday, 10 November, 15:00 – 16:30 CET
Speaker: J. Schilhan, University of Leeds
Title: Entire functions and the continuum
Abstract: In the 60’s, Erdős showed that the continuum hypothesis is equivalent to the statement that there is an uncountable family of entire functions on the complex plane that attains only countably many values at each point. The argument in fact shows that any family of entire functions, that attains at each point less values than elements of that family, must have size continuum. Recently Kumar and Shelah have shown that consistently such a family exists while the continuum has size ℵω1. We answer their main open problem by showing that continuum ℵ2 is possible as well.
This is joint work with T. Weinert.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

CUNY Set Theory Seminar
Time: Friday, 11 November, 12:30pm New York time (18:30 CET)
Speaker: Peter Holy, Technical University of Vienna
Title: Asymmetric Cut and Choose Games
Abstract: We consider the following two player game of infinite length: We are given a starting set X, and the players go by the names ‘Cut’ and ‘Choose’. They take turns making moves, and in each step, Cut partitions a given set into two disjoint pieces, starting from the set X in their first move, and then Choose gets to pick one of the pieces, which is then partitioned into two pieces by Cut in their next move etc. In the end, Choose wins in case the intersection of all of their choices has at least two (distinct) elements.
We will investigate some of the properties of this game — in particular, we will discuss some classic results on when it is possible for one of the players to have a strategy for winning the game. We will then continue to discuss some variations of this game and their relevance to set theory — many central set theoretic notions, such as certain large cardinal properties, notions of distributivity, precipitousness and strategic closure were either known or turned out to be closely connected and often equivalent to the (non-)existence of winning strategies in certain cut and choose games.
This is joint work with Philipp Schlicht, Christopher Turner and Philip Welch (all University of Bristol).
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 11 November, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: David Schrittesser, University of Toronto
Title: tba
Abstract: tba
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

Winter School in Abstract Analysis: 28 Jan – 4 Feb, 2023

We are pleased to announce that registration for the Winter School in Abstract Analysis 2023, section Set Theory & Topology is now open. The conference will take place between Jan 28 and Feb 4 2023. This year the school will be held at Steken Chateau, in South Bohemia, Czech Republic.

Tutorial speakers for this year are:

        Clinton Conley (Carnegie Mellon University)
        Vera Fischer (University of Vienna)
        Aleksandra Kwiatkowska (University of Wroclaw and University of Munster)
        Assaf Rinot (Bar-Ilan University)

Attendees are also invited to contribute research talks.

The early registration conference fee is 10000 CZK (~410 EUR) and covers all expenses, including the bus from Prague to Steken and back. The deadline for payment of the early registration fee is 

        January 4, 2023

After January 4, the conference fee will be 13000 CZK (~530 EUR).

To get more information about the conference and to register please visit our web page:

https://www.winterschool.eu

If you have any questions please do not hesitate to contact us. We hope to see you in January.

Online activities 31 October – 6 November

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

Bristol Logic and Set Theory Seminar
Time:
 Tuesday, 1 November, 12:30-13:30 UK time (13:30-14:30 CEST)
Speaker: Sean Cox, Virginia Commonwealth University
Title: Homological algebra, elementary submodels, and stationary logic
Abstract: The talk will focus on the use of set-theoretic elementary submodel techniques to solve, or partially solve, some problems from homological algebra (independence of Salce’s Problem about cotorsion pairs, and the precovering problem in Gorenstein Homological Algebra).
Information: The login information is posted on the seminar webpage.

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

CMU Core Model Theory Seminar
Time: Tuesday, 1 November, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)  
Speaker:  Derek Levinson
Title: Unreachability of pointclasses in L(R), part 2
Abstract: We present Hjorth’s proof that there is no sequence of distinct 
$\Sigma^1_2$ sets of length $\delta^1_2$. Then we prove in $L(R)$ if 
$\Gamma$ is an inductive-like pointclass then there is no sequence of 
distinct $\Gamma$ sets of length $\delta_\Gamma^+$.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

Helsinki Logic Seminar
Time: Wednesday, 2 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CEST)
Speaker: Miika Hannula
Title: Dependencies and information inequalities
Abstract: Dependence and independence can be interpreted as inequalities over Shannon entropies. In fact, basic principles about dependencies are already at work at the more abstract level of polymatroids, which encapsulate the elementary properties of the entropy function. In this talk we investigate these connections and survey some basic facts about information-theoretic inequalities.
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 2 November, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Sebastian Eterovic, University of Leeds
Title: Strong Existential Closedness
Abstract: The strong existential closedness problem was introduced in Zilber’s work on pseudoexponentiation. Since then, it has been naturally adapted to many situations in arithmetic geometry. In this talk I will introduce the problem, review some important Diophantine questions that are connected to it, and discuss some of the known results.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 2 November, 16:00-17:30 CEST
Speaker: Philipp Lücke, University of Barcelona
Title: Rowbottom cardinals and definability
Abstract: If k is a Rowbottom cardinal, then a short argument shows that
no uncountable ordinal below k is definable by a S1-formula with parameter
k. In my talk, I want to present work that aims to expand this connection
and use undefinability consequences of partition properties to restrict the
class of possible models of set theory in which Àw is a Rowbottom cardinal.
As an example, these results provide a canonical argument that shows that
Àw is not Rowbottom in the standard models of strong forcing axioms.
This is joint work in progress with Omer Ben-Neria (Jerusalem).
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 2 November, 11:00am-12:00pm Pacific time (20:00-21:00 CEST)
Speaker: Dino Rossegger, UC Berkeley
Title: Analytic complete equivalence relations and their degree spectra
Abstract: In this talk, we will show that elementary bi-embeddability is an analytic complete equivalence relation under Borel reducibility by giving a reduction from the bi-embeddability relation on graphs. We will then discuss the degree spectra realized by these relations. The degree spectrum of a countable structure with respect to an equivalence relation EE, a central notion in computable structure theory, is the set of Turing degrees of structures EE-equivalent to it. By analyzing the computability theoretic properties of our reduction from bi-embeddability to elementary bi-embeddability we show that the degree spectra of these two relations are related. Suppose a set of Turing degrees XX is the bi-embeddability spectrum of a graph. Then the set of degrees whose Turing jump is in XX is the elementary bi-embeddability spectrum of a graph. Combining results of Harrison-Trainor and the coauthor one sees that this is sharp: There is a bi-embedddability spectrum that is not an elementary bi-embeddability spectrum.
Information: Please see the seminar webpage.

Vienna Logic Colloquium
Time:
 Thursday, 2 November, 15:00 – 16:30 CET
Speaker: W. Brian, University of North Carolina at Charlotte
Title: Covering versus partitioning with Polish spaces
Abstract: A topological space is Polish if it is second countable and completely metrizable. We may think of these as the small, or “essentially countable” members of the category of completely metrizable spaces. In this talk, we explore the question of whether, given a completely metrizable space X, it is possible to cover X with fewer Polish spaces than it can be partitioned into. Surprisingly, this question not only turns out to be independent of ZFC, but proving its independence requires large cardinal axioms. I will sketch some of the ideas that go into one direction of this independence proof. Specifically, I will describe how a version of the model-theoretic transfer principle called Chang’s Conjecture implies that there is a completely metrizable space that can be covered with fewer Polish spaces than it can be partitioned into.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Vienna Research Seminar in Set Theory
Time: Thursday, 3 November, 16:45-18:15 CEST – note the time change
Speaker: W. Brian, University of North Carolina at Charlotte
Title: Partitioning the real line into Borel sets
Abstract: I will sketch a proof that, assuming 0† does not exist, if there is a partition of the real line R into ℵω Borel sets, then there is also a partition of R into ℵω+1 Borel sets. (And the same is true for any singular cardinal of countable cofinality in place of ℵω.) This contrasts starkly with the situation for successor-of-successor cardinals, where the spectrum of possible sizes of partitions of Rinto Borel sets can seemingly be made completely arbitrary. For example, given any A⊆ω with 0,1∈A, there is a forcing extension in which A={n<ω: there is a partition of R into ℵn Borel sets}.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 4 November, 16.00-17.00 CEST
Speaker: J. Emmenegger, University of Genoa
Title: Quotients and equality, (co)algebraically
Abstract: Doctrines were introduced by Lawvere as an algebraic tool to work with logical theories and their extensions. In fact, this algebraic character makes the theory of doctrines a suitable context where to address the question: “”What is the theory obtained by (co)freely adding logical structure?”” or the closely related question: “”How to express additional logical structure in terms of what is already available?””. More precisely, in the first case we ask whether a certain forgetful functor is adjoint and, in the second case, whether the adjunction obtained in this way is (co)monadic. After an introduction to doctrines and their connection to logic and type theory, I shall discuss the above questions in the case of two forgetful functors: the one from theories with conjunctions, equality and quotients to theories with conjunctions and equality, and the one that further forgets equality. Not surprisingly, the answers revolve around the concept of equivalence relation. I shall discuss applications to useful constructions in categorical logic and type theory, as well as to the theory of imaginary elements in the sense of Poizat. If time allows, I shall also describe how to lift this setting to Grothendieck fibrations (of which doctrines are a particular case) using groupoids instead of equivalence relations.
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, 4 November, 12:30pm New York time (18:30 CEST)
Speaker: Corey Switzer, University of Vienna
Title: The Special Tree Number
Abstract: A tree of height ω1 with no cofinal branch is called special if it can be decomposed into countably many antichains or, equivalently if it carries a specializing function: a function f:T→ω so that if f(s)=f(t) then s and t are incomparable in the tree ordering. It is known that there is always a non-special tree of size continuum, but the existence of a smaller one is independent of ZFC. Motivated by this we introduce the special tree number, st, the least size of a tree of height ω1which is neither non-special nor has a cofinal branch. Classical facts imply that st can be smaller than essentially all well studied cardinal characteristics. Conversely in this talk we will show that stcan be larger than a, g, and both the left hand side and bottom row of the Cichon diagram. Thus stis independent of many well known cardinal invariants. Central to this result is an in depth investigation of the types of reals added by the Baumgartner specialization poset which we will discuss as well.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 4 November, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Vinicius De Oliveira Rodrigues
Title: Fin-intersecting MAD families and the pseudocompactness of hyperspaces
Abstract: We study Ginsburg’s questions on the relations between the pseudocompactness of the Vietoris hyperspace of a given topological space and the pseudocompactness of its powers restricted to the context of Isbell-Mrówka space. An almost disjoint family is said to be pseudocompact if the Vietoris Hyperspace of its Isbell-Mrówka space is pseudocompact. In the context of Isbell-Mrówka spaces, Ginsburg’s questions become questions about the existence of pseudocompact MAD families. We will discuss what has been done around this problem and what remains open. To further study this problem we propose a new class of almost disjoint families which we call fin-intersecting almost disjoint families. Every fin intersecting MAD family is pseudocompact. Under p=c such families exist generically, but there is also a MAD pseudocompact family which is not fin-intersecting. Also, under CH, forcing extensions obtained by adding Cohen reals and Random reals contain such families.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 4 November, 2:00 – 3:30 New York time (20:00-21:30 CEST)
Speaker: Dave Marker, University of Illinois at Chicago
Title: Automorphisms of differentially closed fields
Abstract: Answering a question of Russell Miller, we show that there are differentially closed fields with no non-trivial automorphisms.
Information: The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.

Online activities 24-30 October

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

Special event (for details see below):
Thursday, 27 October, 17:00-19:00 CEST
European Set Theory Society Panel Discussions
Panelists: Michael Hrusak, Juliette Kennedy, Menachem Magidor, Justin Tatch Moore
Zoom link for 27 October: https://univienna.zoom.us/j/62758810753?pwd=cFJkZjVWMGpmWmtKWUd4UE1EdXQ1dz09
Meeting-ID: 627 5881 0753, Code: est22

Vienna Research Seminar in Set Theory
Time: Tuesday, 25 October, 15:00-16:30 CEST
Speaker: Diana Carolina Montoya, University of Vienna
Title: Maximal independence and singulars
Abstract: In these talks, we will discuss the concept of maximal independent families for uncountable singular cardinals. In the first part, I will present the existing background results in the regular case from Kunen and Eskew-Fischer. In the second part, we will focus on the joint results obtained in joint work with Omer Ben-Neria: some on the existence of maximal independent families at a singular strong limit, and finally some on the possible sizes of such families.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

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

CMU Core Model Theory Seminar
Time: Tuesday, 25 October, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CEST)  
Speaker:  Derek Levinson
Title: Unreachability of pointclasses in L(R), part 1
Abstract: We present Hjorth’s proof that there is no sequence of distinct
$\Sigma^1_2$ sets of length $\delta^1_2$. Then we prove in $L(R)$ if
$\Gamma$ is an inductive-like pointclass then there is no sequence of
distinct $\Gamma$ sets of length $\delta_\Gamma^+$.
Information: Please contact Ernest Schimmerling in advance for the zoom link.

CMU Logic Seminar
Time: Tuesday, 25 October,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)  
Speaker:  Kristin Yvonne Rozier, Iowa State University
Title: Proofs that Fly! Logic, Automata, and Set Theory in Air and Space
Abstract: We are at the dawn of the age of unmanned aircraft, automated air traffic control, and autonomous spacecraft, where safe operation remains the primary consideration. Before we can build or deploy such safety-critical systems we must formally prove that they always satisfy safety requirements. Such certification critically depends on logic, automata, and set theory! We directly employ these techniques to formalize aerospace operational concepts: we must unambiguously specify safety requirements to produce automated, re-playable proofs that safety-critical systems behave the way we expect them to, before we allow them to interact with humans. Techniques from set theory and graph theory enable the scalability required to analyze a large (20K+) set of possible air traffic control designs from NASA. We address areas for future collaborations: what are the next big questions we must answer to proceed safely from here?
Information: See the seminar webpage.

Leeds Models and Sets Seminar
Time: Wednesday, 26 October, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Andrew Brooke-Taylor, University of Leeds
Title: Cardinal characteristics modulo nice ideals on omega
Abstract: Many of the standard cardinal characteristics of the continuum are defined in terms of a relation holding almost everywhere, where “almost everywhere” means on all but a finite set. A very natural generalisation is to take “almost everywhere” to mean on all but a member of a given ideal.  I will talk about what happens when we do this, with the density 0 ideal on omega as a focal example.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 26 October, 16:00-17:30 CEST
Speaker: Juan P. Aguilera
Title: Determinacy on the Edge of Second-Order Arithmetic
Abstract: We calculate the exact strength of the strongest theories of determinacy which are provable in Second-Order Arithmetic, answering a question of Montalbán. This is joint work with Philip Welch.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Caltech Logic Seminar
Time: Wednesday, 26 October, 11:00am-12:00pm Pacific time (20:00-21:00 CEST)
Speaker: Andy Zucker, University of Waterloo
Title: Big Ramsey degrees and Galvin-Prikry theorems for binary free-amalgamation classes
Abstract: Given a finite relational language L and a (possibly infinite) set F of finite irreducible L-structures, the class Forb(F) describes those finite L-structures which do not embed any member of F. Classes of the form Forb(F) exactly describe those classes of finite L-structures with free amalgamation. In recent joint work with Balko, Chodounsky, Dobrinen, Hubicka, Konecny, and Vena, we exactly characterize big Ramsey degrees for those classes Forb(F) where the forbidden set F is finite. This characterization proceeds by defining tree-like objects called diagonal diaries, then showing that the big Ramsey degree of any A in Forb(F) is exactly the number of diagonal diaries which code the structure A. After giving a brief description of these objects, the talk will then consider those infinite diagonal diaries which code the Fraisse limit of Forb(F). In upcoming joint work with Dobrinen, we prove a Galvin-Prikry theorem for any such infinite diagonal diary, giving new examples of objects satisfying the Galvin-Prikry theorem which dramatically fail to satisfy Todorcevic’s Ramsey space axioms A1 through A4.
Information: Please see the seminar webpage.

European Set Theory Society Panel Discussions
Time: Thursday, 27 October, 17:00-19:00 CEST
Panelists: Michael Hrusak, Universidad Nacional Autónoma de México
Juliette Kennedy, University of Helsinki
Menachem Magidor, Hebrew University of Jerusalem
Justin Tatch Moore, Cornell University
Title: European Set Theory Society Panel Discussions
Abstract: Four experts will be invited to describe the general area they represent, explain where the area is heading and discuss how it relates to other areas of set theory and mathematics.
Information: Online. Zoom link for 27 October: https://univienna.zoom.us/j/62758810753?pwd=cFJkZjVWMGpmWmtKWUd4UE1EdXQ1dz09 , Meeting-ID: 627 5881 0753, Code: est22

CUNY Set Theory Seminar
Time: Friday, 28 October, 12:30pm New York time (18:30 CEST)
Speaker: Andreas Lietz, University of Münster
Title: Forcing ‘NSω1 is ω1-dense’ from Large Cardinals – A Journey guided by the Stars: Part II
Abstract: An ideal I on ω1 is ω1-dense if (P(ω1)/I)+ has a dense subset of size ω1. We prove, assuming large cardinals, that there is a semiproper forcing P so that VP⊨‘NSω1 is ω1-dense’. This answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of Pmax in Woodin’s axiom (∗) by Qmax results in an axiom Qmax−(∗) which implies ‘NSω1 is ω1-dense’.
We proceed in three steps: First we define and motivate a new forcing axiom QM and then modify the Asperó-Schindler proof of ‘MM++⇒(∗)’ to show ‘QM⇒Qmax−(∗)’. Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing QM. This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 28 October, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Andy Zucker, University of Waterloo
Title: Galvin-Prikry theorems for big Ramsey structures
Abstract: The Galvin-Prikry theorem, an infinite-dimensional generalization of the infinite Ramsey theorem, can be stated in the language of semigroups as follows: for any finite Borel partition of the semigroup of monotone injections from ω into itself, one piece contains a right ideal. This talk provides a generalization of this result to the semigroups of embeddings of certain more complicated first-order structures. The definition and construction of these structures arise from the study of big Ramsey degrees in binary free amalgamation classes. This is joint work with Natasha Dobrinen.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 28 October, 2:00 – 3:30 New York time (20:00-21:30 CEST)
Speaker: Corey Switzer, University of Vienna
Title: Ideal Independence, Filters and Maximal Sets of Reals
Abstract: A family I⊆[ω]ω is called ideal independent if given any finite, distinct A,B0,…,Bn−1∈I, the set A∖⋃i<nBi is infinite. In other words, the ideal generated by I∖{A} does not contain A for any A∈I. The least size of a maximal (with respect to inclusion) ideal independent family is denoted smm and has recently been tied to several interesting questions in cardinal characteristics and Boolean algebra theory. In this talk we will sketch our new proof that this number is ZFC-provably greater than or equal to the ultrafilter number – the least size of a base for a non-principal ultrafilter on ω. The proof is entirely combinatorial and relies only on a knowledge of ultrafilters and their properties. Time permitting, we will also discuss some interesting new applications of ideal independent families to topology via a generalization of Mrowka spaces usually studied for almost disjoint families. This is joint work with Serhii Bardyla, Jonathan Cancino and Vera Fischer.
Information: The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.

Online activities 17-23 October

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

Vienna Research Seminar in Set Theory
Time: Tuesday, 18 October, 15:00-16:30 CEST
Speaker: Diana Carolina Montoya, University of Vienna
Title: Maximal independence and singulars
Abstract: In these talks, we will discuss the concept of maximal independent families for uncountable singular cardinals. In the first part, I will present the existing background results in the regular case from Kunen and Eskew-Fischer. In the second part, we will focus on the joint results obtained in joint work with Omer Ben-Neria: some on the existence of maximal independent families at a singular strong limit, and finally some on the possible sizes of such families.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

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

Helsinki Logic Seminar
Time: Wednesday, 19 October, 12:00 – 14:00 Helsinki time (11:00-13:00 CEST)
Speaker: Davide Quadrellaro
Title: Weak Dependence Logic
Abstract: We introduce and study a fragment of dependence logic which we call weak dependence logic. The interest in this fragment lays in the fact that, although it is much less expressive than full dependence logic, it has three desirable features:
(i) a strong form of compactness;
(ii) the De Jongh property w.r.t. propositional dependence logic;
(iii) it admits a notion of model-theoretic type which gives rise to Esakia spaces.
We show these properties and establish connections to the algebraic and topological semantics of propositional dependence logic.
Information: The talk will take place in hybrid mode. Please see the seminar webpage for the link.

Leeds Models and Sets Seminar
Time: Wednesday, 19 October, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Philipp Schlicht, University of Bristol
Title: Interaction of determinacy and forcing
Abstract: Determinacy principles provide a unified theory of definable sets of reals beyond Borel and analytic sets, while forcing is an important technique to study the independence of properties of sets of reals. This suggests studying the interaction of the two: how robust are determinacy principles under well behaved forcings? I will talk about the history of this problem as well as recent joint results with Jonathan Schilhan and Johannes Schürz on iterations of proper forcings. A sample application of our results is the following: starting from a model of analytic determinacy, one can construct a model of analytic determinacy and the Borel conjecture.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 19 October, 16:00-17:30 CEST
Speaker: Christopher Turner, University of Bristol
Title: Lowenheim-Skolem-Tarski Numbers for Regularity Quantifiers
Abstract: Let Q1, …, Qn be quantifiers of second-order logic. The Lowenheim-Skolem-Tarski number LST(Q0, … ,Qn) is the smallest cardinal kappa such that for any first order structure A in a language of size less than kappa, there exists a substructure B<A of size less than kappa, which is elementary in the language L U {Q0, …, Qn}. In 2011, Magidor and Väänänen found exact lower bounds for two important second order quantifiers: the Härtig quantifier I, and the equal cofinality quantifier Qec. Informally, I tells us about the cardinals of V, and Qec tells us which of them are V-inaccessible. In this talk I will present a generalisation of these to the two schemes of intermediate quantifiers Qa and Ra. These two quantifiers (which are defined for any ordinal a) fit between I and Qec, telling us about precisely the inaccessibles with Cantor-Bendixson rank less than a. I will introduce the quantifiers, and examine how their LST numbers relate to each other and to the LST numbers for I and Qec. I will then give a lower bound for each of the LST numbers. Finally, I will sketch a proof that this bound is exact, assuming the consistency of supercompacts.
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
Time:
 Thursday, 20 October, 10:30-11:30 UK time (11:30-12:30 CEST) – note the time change
Speaker: Frank Stephan, National University of Singapore
Title: Initial Segment Complexity for Measures
Abstract: Based on a joint paper with Andre Nies (https://arxiv.org/abs/1902.07871), the speaker will present the background and selected results of the paper. Furthermore, the slides are available here: https://www.comp.nus.edu.sg/~fstephan/measurerandomtalkslides.pdf.
Information: The login information is posted on the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, 21 October, 12:30pm New York time (18:30 CEST)
Speaker: Andreas Lietz, University of Münster
Title: Forcing ‘NSω1 is ω1-dense’ from Large Cardinals – A Journey guided by the Stars
Abstract: An ideal I on ω1 is ω1-dense if (P(ω1)/I)+ has a dense subset of size ω1. We prove, assuming large cardinals, that there is a semiproper forcing P so that VP⊨‘NSω1 is ω1-dense’. This answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of Pmax in Woodin’s axiom (∗) by Qmax results in an axiom Qmax−(∗) which implies ‘NSω1 is ω1-dense’.
We proceed in three steps: First we define and motivate a new forcing axiom QM and then modify the Asperó-Schindler proof of ‘MM++⇒(∗)’ to show ‘QM⇒Qmax−(∗)’. Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing QM. This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 21 October, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Shaun Allison, University of Toronto
Title: The classification strength of Polish groups
Abstract: We reframe much of the study of Borel reductions between orbit equivalence relations as the study of the classification strength of Polish groups. This is a partial order where we say G is stronger than H iff every orbit equivalence relation induced by a continuous action of H on a Polish space is Borel reducible to such an orbit equivalence relation induced by G. We discuss recent results pertaining to the non-Archimedean Polish groups with maximum classification strength, namely, the groups which involve S_infty. We give several surprising conditions which are equivalent to involving S_infty. Time permitting, we will discuss other work on other parts of the hierarchy of classification strength, including joint work with Aristotelis Panagiotopoulos.
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

CUNY Logic Workshop
Time: Friday, 21 October, 2:00 – 3:30 New York time (20:00-21:30 CEST)
Speaker: Philipp Rothmaler, CUNY
Title: Generalized Bass modules
Abstract: Over half a century ago Hyman Bass proved that all flat left modules are projective precisely when the underlying ring satisfies the descending chain condition on right principal ideals. He called such rings left perfect. Gena Puninski noticed that this can be given a model theoretic proof. Every infinite descending chain of principal right ideals gives rise to a descending chain of (pp) formulas which, in turn, gives rise to a direct limit of finitely generated projective modules that is not projective. Such a module is flat and not projective, and called a Bass module.
I demonstrate how this construction is elementary model theory and at the same time generalizes to other classes of (pp) formulas and modules, which, among other things, yields a new proof of the late Daniel Simson’s result that all left modules are Mittag-Leffler iff the ring is left pure-semisimple (which, to model theorists, means that all left modules are totally transcendental).
I will emphasize the model theoretic ideas and explain the connection with the algebraic concepts. This is part of ongoing work with Anand Pillay.
Information: The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.