# Online Activities 18-24 January

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

Paris-Lyon Séminaire de Logique
Time:
Wednesday, 20 January, 16:00-17:00 CEST
Speaker: Gianluca Basso, University of Lyon
Title: Compact metrizable structures via projective Fraïssé theory
Abstract: The goal of projective Fraïssé theory is to approximate compact metrizable spaces via classes of ﬁnite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. We will discuss general results, using the framework of compact metrizable structures, as well as applications to the study a class of one-dimensional compact metrizable spaces, that of smooth fences, and to a particular smooth fence with remarkable properties, which we call the Fraïssé fence.
Information: Join via the link on the seminar webpage 10 minutes before the talk.

Barcelona Set Theory Seminar
Time: Wednesday, 20 January, 16:00-17:30 CET
Speaker: Vera Fischer, University of Vienna
Title: Independent families in the countable and the uncountable
Abstract: Independent families on w are families of infinite sets of integers with the property that for any two finite subfamilies A and B the set Ç A\È B is infinite. Of particular interest are the sets of the possible cardinalities of maximal independent families, which we refer to as the spectrum of independence. Even though we do have the tools to control the spectrum of independence at w (at least to a large extent), there are many relevant questions regarding higher counterparts of independence in generalised Baire spaces still remaining open.
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, 20 January, 16:00-17:30 UK time (17:00-18:30 CEST)
Speaker: Dima Sinapova, University of Illinois at Chicago
Title: Iteration, reflection, and singular cardinals
Abstract: Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$, and
(2) from large cardinals it is consistent to have the failure of SCH at $\aleph_\omega$.These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_\omega$. This is joint work with Alejandro Poveda and Assaf Rinot.

Caltech Logic Seminar
Time: Wednesday, 20 January, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Todor Tsankov, Université Lyon 1
Title: Universal minimal flows of homeomorphism groups of high-dimensional manifolds
Abstract: The first interesting case of a non-trivial, metrizable universal minimal flow (UMF) of a Polish group was computed by Pestov who proved that the UMF of the homeomorphism group of the circle is the circle itself. This naturally led to the question whether a similar result is true for homeomorphism groups of other manifolds (or more general topological spaces). A few years later, Uspenskij proved that the action of a group on its UMF is never 3-transitive, thus giving a negative answer to the question for a vast collection of topological spaces. Still, the question of metrizability of their UMFs remained open and he asked specifically whether the UMF of the homeomorphism group of the Hilbert cube is metrizable. We give a negative answer to this question for the Hilbert cube and all closed manifolds of dimension at least 2, thus showing that metrizability of the UMF of a homeomorphism group is essentially a one-dimensional phenomenon. This is joint work with Yonatan Gutman and Andy Zucker.
Information: See the seminar webpage.

KGRC Research Seminar, Vienna
Time:
Thursday, 21 January, 15:00-16:30 CET
Speaker: Juris Steprans, York University, Toronto, Canada
Title: Strong colourings over partitions
Abstract: The celebrated result of Todorcevic that ℵ1↛[ℵ1]2ℵ1 provides a well known example of a strong colouring. A mapping c:[ω1]2→κ is a strong colouring over a partition p:[ω1]2→ω if for every uncountable X⊆ω1 there is n∈ω  such that the range of c on [X]2∩p−1{n} is all of κ. I will discuss some recent work with A. Rinot and M. Kojman on negative results concerning strong colourings over partitions and their relation to classical results in this area.
Information: Talk via zoom.

Toronto Set Theory Seminar
Time: Friday, 21 January, 11:00am-12:30pm Toronto time (17:00-18:30 CET)
Speaker: Dima Sinapova, UIC, University of Illinois at Chicago
Title: Iteration, reflection, and singular cardinals
Abstract: Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at  $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at  $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.
Information: Email Ivan Ongay Valverde ahead of time for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 22 January, 2pm New York time (20:00 CET)
Speaker: Erin Carmody, Fordham University
Title: The relationships between measurable and strongly compact cardinals
Abstract: This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor’s identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where κ1 and κ2 are the first and second strongly compact cardinals, respectively, and where κ1 is least with Mitchell order 1, and κ2is the least with Mitchell order 2. Another main theorem is that there is a universe where κ1 and κ2are the first and second strongly compact cardinals, respectively, with κ1 the least measurable cardinal such that o(κ1)=2 and κ2 the least measurable cardinal above κ1. This is a joint work in progress with Victoria Gitman and Arthur Apter.
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 January, 1:30-3pm Toronto time (19:30-21:00 CET)
Speaker: Marcos Mazari Armida, Carnegie Mellon University
Title: Universal models in classes of abelian groups and modules
Abstract: The search for universal models began in the early  twentieth century when Hausdorff showed that there is a  universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to  pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.
Information: Email Ivan Ongay Valverde ahead of time for the zoom link.

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# Set Theory Workshop, Sao Paulo

This is an event organized as a celebration of the World Logic Day (January 14th) as proclaimed by UNESCO in association with the International Council for Philosophy and Human Sciences (CIPSH).

https://www.ime.usp.br/~spld2021/

## List of Speakers

• Christina Brech (São Paulo)
• Vera Fischer (Vienna)
• Yurii Khomskii (Hamburg & Amsterdam)
• Victor dos Santos Ronchim (São Paulo)
• Dorottya Sziráki (Budapest)
• Artur Hideyuki Tomita (São Paulo)

## Book of Abstracts

The book of abstracts may be found here.

## Registration

There is no registration fee for this conference. For registration, please fill this form with your name, affiliation and e-mail. After registration, you will receive a link to the Zoom webinar.

## Preliminary schedule

The event will be held on January 14th.

Brazilia Standard Time (GMT -3):

• 09:00 – 09:10 – Reception
• 09:10 – 09:55 – Christina Brech
• 10:00 – 10:45 – Dorottya Sziráki
• 11:00 – 11:45 – Victor dos Santos Ronchim
• 13:00 – 13:45 – Vera Fischer
• 13:50 – 14:35 – Artur Hideyuki Tomita
• 14:50 – 15:35 – Yurii Khomskii

Greenwich Mean Time (GMT):

• 12:00 – 12:10 – Reception
• 12:10 – 12:55 – Christina Brech
• 13:00 – 13:45 – Dorottya Sziráki
• 14:00 – 14:45 – Victor dos Santos Ronchim
• 16:00 – 16:45 – Vera Fischer
• 16:50 – 17:35 – Artur Hideyuki Tomita
• 17:50 – 18:35 – Yurii Khomskii

# Online activities 11-17 January

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

Genova logic seminar
Time: Monday, 11 January, 15.00-16.30 CET
Speaker: Filippo Calderoni, University of Illinois at Chicago
Title: Categorifying Borel reducibility
Abstract: The theory of Borel classification is a central research area in modern descriptive set theory. It provides a logical treatment to the process of classification and has been used effectively in different areas of mathematics as a tool to detect structural obstructions against classification theorems. The idea of making Borel reducibility functorial goes back to the start of the area, being raised already in one of the initial papers by Friedman and Stanley. In this talk we will discuss yet another attempt to formalize Borel reducibility in a categorical framework. This is joint work in progress with Andrew Brooke-Taylor.
Information: The seminar will be held on Microsoft Teams, at the page of the Genoa logic group. The access code is: fpedcxn. Alternatively, you can write to camerlo@dima.unige.it to have an access link. Further information on the activities of the Genoa logic group can be
found at logic.dima.unige.it

Caltech Logic Seminar
Time: Monday, 11 January, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Zoltán Vidnyánszky, Caltech
Title: A new regularity property of the Haar null ideal
Abstract: Christensen’s Haar null ideal is a well-behaved generalization of Haar null sets to groups, which admit no Haar measure. We show that in the group ZωZω, every Haar positive (that is, non-Haar null) analytic set contains a Haar positive closed set. Using this result, we determine the exact Wadge class of the family of Haar null closed subsets of ZωZω.
Information: See the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 13 January, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Juris Steprans, York University, Toronto
Title: Universal functions, strong colourings and ideas from PID
Abstract: A construction of Shelah will be reformulated using the PID to provide alternative models of the failure of CH and the existence of a universal colouring of cardinality aleph_1. The impact of the range of the colourings will be examined. An application to the theory of strong colourings over partitions will
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 13 January, 16:00-17:30 CET
Speaker: Trevor Wilson, Miami University
Title: tba
Abstract: tba
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Set theory workshop Sao Paulo, for the World Logic Day
Time:
Thursday, 14 January, 9:00-18:35 Brazil time (13:00-22:35 CET)
Speakers: Christina Brech (São Paulo), Vera Fischer (Vienna), Yurii Khomskii (Hamburg , Victor dos Santos Ronchim (São Paulo), Dorottya Sziráki (Budapest), Artur Hideyuki Tomita (São Paulo)

KGRC Research Seminar, Vienna
Time:
Thursday, 14 January, 15:00-16:30 CET
Speaker: Jeffrey Bergfalk, University of Vienna
Title: Infinitary combinatorics and strong homology
Abstract: Motivated by several recent advances, we will provide a research history of the main set-theoretic problems arising in the study of strong homology. As such, this talk will overlap with one on the same theme given in Paris-Lyon Logic Seminar last fall. We will presume no awareness in our audience either of strong homology or of that talk, but will aim in this one to provide, along with the necessary background, some sketch of the main ideas behind several recent arguments. This is an area in which simplicial principles and infinitary combinatorics come together. Its questions, at heart, have tended to be questions about higher-dimensional variants of classical set-theoretic concerns (like nontrivial coherence, Δ systems, etc.); these questions, in turn, increasingly appear to be of some interest in their own right.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 15 January, 16:30-18:30 CET
Title: Ackermann, Goodstein, and infinite sets
Abstract: In this talk, I show how Goodstein’s classical theorem can be turned into a statement that entails the existence of complex infinite sets, or in other words: into an object of reverse mathematics. This more abstract approach allows for very uniform results of high explanatory power. Specifically, I present versions of Goodstein’s theorem that are equivalent to arithmetical comprehension and arithmetical transfinite recursion. To approach the latter, we will study a functorial extension of the Ackermann function to all ordinals. The talk is based on a joint paper with J. Aguilera, M. Rathjen and A. Weiermann.
Information: Online on WebEx. Please see the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, January 15, 2pm New York time (20:00 CET)
Speaker: Trevor Wilson, Miami University
Title: tba
Abstract: tba
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

# Online activities 4-10 January

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

Turin logic seminar
Time: Friday, 8 January, 09.30-10.30 CET
Speaker: A. Conversano, Massey, New Zealand
Title: Model theory and groups
Abstract: tba
Information: Online. Please see the seminar webpage.

Turin-Udine logic seminar
Time: Friday, 8 January, 16:30-18:30 CET
Speaker: F. Calderoni, University of Illinois at Chicago
Title: The Borel structure on the space of left-orderings
Abstract: In this talk we shall present some results on left-orderable groups and their interplay with descriptive set theory. We shall discuss how Borel classification can be used to analyze the space of left-orderings of a given countable group modulo the conjugacy action. In particular, we shall see that if G is not locally indicable then the conjugacy relation on LO(G) is not smooth. Also, if G is a nonabelian free group, then the conjugacy relation on LO(G) is a universal countable Borel equivalence relation. Our results address a question of Deroin-Navas-Rivas and show that in many cases LO(G) modulo the conjugacy action is nonstandard. This is joint work with A. Clay.
Information: Online on WebEx. Please see the seminar webpage.

CUNY Set Theory Seminar
Time: Friday, 8 January, 2pm New York time (20:00 CET)
Speaker: Thilo Weinert, University of Vienna
Title: A miscellany of observations regarding cardinal characteristics of the continuum
Abstract: We are going to talk about some inequalities between cardinal characteristics of the continuum. In particular we are going to relate cardinal characteristics pertaining to the convergenve of series, recently isolated by Blass, Brendle, Brian and Hamkins, other characteristcs concerning equitable splitting defined comparatatively recently by Brendle, Halbeisen, Klausner, Lischka and Shelah and some characteristics defined less recently by Miller, Blass, Laflamme and Minami. All proofs in question are elementary.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

# Online Activities 28 December 2020 – 3 January 2021

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 30 December, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Assaf Shani, Harvard
Title:  Actions of tame abelian product groups
Abstract: A Polish group G is tame if for any continuous action of G, the corresponding orbit equivalence relation is Borel. Suppose that G=\prod_n \Gamma_n is a product of countable abelian groups. It follows from results of Solecki and Ding-Gao that if G is tame, then all of its actions are in fact potentially \Pi^0_6. Ding and Gao conjectured that this bound could be improved to \Pi^0_3. We refute this, by finding an action of a tame abelian product group, which is not potentially \Pi^0_5. The proof involves forcing over models where the axiom of choice fails for sequences of finite sets. This is joint work with Shaun Allison.
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

# Online Activities 21-27 December

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 23 December, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Roy Shalev, Bar Ilan University
Title: A guessing principle from a Souslin tree, with applications to topology
Abstract: We introduce a new combinatorial principle which we call ♣_AD. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out de Caux type constructions of topological spaces.
Our main result states that strong instances of ♣_AD follow from the existence of a Souslin tree.  As an application, we obtain a simple, de Caux type proof of Rudin’s result that if there is a Souslin tree, then there is an S-space which is Dowker.
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

# Online Activities 14-20 December

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 16 December, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Roy Shalev, Bar Ilan University
Title: S spaces and L spaces, part 1
Abstract: It will be both a survey talk and exposition of new results. Very likely it will be continued the following week.
An S-space is a regular topological space that is hereditarily separable but not Lindel\”of. An L-space is a regular topological space that is hereditarily Lindel\”of but not separable. We will survey the history behind the question of their existence and present some constructions.
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 16 December, 16:00-17:30 CET
Speaker: Victoria Gitman, CUNY
Title: Characterizing large cardinals via abstract logics
Abstract: First-order logic, the commonly accepted formal system underlying mathematics, must draw however minimally on the properties of the set-theoretic universe in which it is defined. Stronger logics such as infinitary logics and second-
order logics require access to much larger chunks of the set-theoretic background. Niceness properties of these logics, such as forms of compactness, are naturally
connected to the existence of large cardinals. Indeed, many large cardinals can be
characterized in terms of compactness properties of strong logics. Strongly compact
and weakly compact cardinals k are precisely the strong and weak compactness
cardinals respectively for the infinitary logic Lkk. Extendible cardinals k are precisely
the strong compactness cardinals for the infinitary second-order logic \$\mathbb L2
kk. Vopenka’s Principle holds if and only if every logic has a strong compactness cardinal. In this talk I will review properties of various logics and how their compactness
properties characterize various large cardinals. I will discuss joint work with Will Boney, Stamatis Dimopoulos and Menachem Magidor in which we show that the principle Ord is subtle, in the presence of global choice, holds if and only if every logic
has a weak compactness cardinal, i.e., it is the analogue of Vopenka’s Principle for weak compactness. We also provide characterizations of the various virtual large cardinals using a new notion of a pseudo-model of a theory.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Münster research seminar on set theory
Time: Wednesday, 16 December, 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.

Caltech Logic Seminar
Time: Wednesday, 16 December, 12:00 – 1:00pm Pacific time (22:00 CET)
Speaker: Martino Lupini, Victoria University of Wellington
Title: Classification of extension of C*-algebras and K-homology
Abstract: I will present an introduction from the perspective of Borel complexity theory to the classification problem for extension of C*-algebras, its motivations from operator theory, and its connections with homological algebra.
Information: See the seminar webpage.

KGRC Research Seminar
Time:
Thursday, 17 December, 15:00 CET
Speaker: Peter Holy, University of Udine
Title: Ramsey-like Operators
Abstract: Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 18 December, 16:30pm CET
Speaker: Monroe Eskew, University of Vienna
Title: Weak square from weak presaturation
Abstract: Can we have both a saturated ideal and the tree property on ℵ2? Towards the negative direction, we show that for a regular cardinal κ, if 2<κ≤κ+ and there is a weakly presaturated ideal on κ+ concentrating on cofinality κ, then □∗κ holds. This partially answers a question of Foreman and Magidor about the approachability ideal on ℵ2. A surprising corollary is that if there is a presaturated ideal J on ℵ2 such that P(ℵ2)/J is a semiproper forcing, then CH holds. This is joint work with Sean Cox.
Information: Please see the seminar webpage.

# Master and PhD fellowships in mathematics in Paris

__________________________________ PhD Cofund MathInParis2020 _______________________________

The international Doctoral Training in Mathematical Sciences in Paris MathInParis2020, cofunded by European Commission’s Marie Sklodowska-Curie Actionsoffers 20 PhD fellowships for academic year 2021-2022. The positions are located in Paris.

Call for applications: from Tuesday December 1st 2020 to Saturday February 13th 2021 at 11:59 p.m., Paris time.

Offer description:  https://www.sciencesmaths-paris.fr/fr/cofund-mathinparis-842.htm

_____________________________________PGSM _______________________________________________

The PGSM program of the Fondation Sciences Mathématiques de Paris offers master scholarships in Mathematics and in fundamental Computer Science for academic year 2021-2022. The positions are located in Paris. Schedule of deadlines below (at 11:59 p.m., Paris time). Feel free to circulate this message to your contacts.

1st call: before Friday January 22nd 2021.  Only for students from universities out of France.

2nd call: from Tuesday December 1st 2020 to Saturday May 8th 2021. Open to the same students plus those from universities of FSMP’s network.

Offer description:  https://www.sciencesmaths-paris.fr/en/masters-250.htm

# Online Activities 7-12 December

Computability and application seminar
Time: Tuesday, 8 December, 22:00 CET
Speaker: Linda Brown Westrick, Pennsylvania State University
Title: Luzin’s (N) and randomness reflection
Abstract: Tba
Information: The seminar will take place virtually via zoom.

Münster research seminar on set theory
Time: Wednesday, December 9, 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, December 9, 16:00 CET
Speaker: Neil Barton, University of Konstanz
Title: Intensional classes and intuitionistic topoi
Abstract: A popular view in the philosophy of set theory is that of potentialism: the position that the set-theoretic universe unfolds as more sets come into existence. A difficult question for the potentialist is to explain how classes (understood as intensional entities) behave on this framework, and in particular what logic governs them. In this talk we’ll see how category-theoretic resources can be brought to bear on this issue. I’ll first give a brief introduction to topos theory, and then I’ll explain how (drawing on work of Lawvere) we can think of intensional classes for the potentialist as given by a functor category. I’ll suggest some tentative directions for research here, including the possibility that this representation indicates that the logic of intensional classes should be intuitionistic rather than classical, and that the strength of the
intuitionistic logic is dependent upon the partial order on the worlds.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Paris-Lyon Séminaire de Logique
Time:
Wednesday, December 9, 16:00-17:00 CET
Speaker: Andrea Vaccaro, IMJ-PRG
Title: Set Theory and the Endomorphisms of the Calkin algebra
Abstract: Set theory induces a sharp dichotomy in the structure of the set of automorphisms of the Calkin algebra Q(H): under the Open Coloring Axiom (OCA) all the automorphisms of Q(H) are inner (Farah, 2011), whereas the Continuum Hypothesis (CH) implies that there exist uncountably many outer automorphisms of Q(H) (Phillips-Weaver, 2007). After a brief introduction on the line of research that led to these results, I’ll discuss how this dichotomic behavior extends to the semigroup End(Q(H)) of unital endomorphisms of Q(H). In particular, we’ll see that under OCA all unital endomorphisms of Q(H) can be, up to unitary equivalence, lifted to unital endomorphisms of B(H). This fact allows to have an extremely clean picture of End(Q(H)), and has some interesting consequences concerning the class of C*-algebras that embed into Q(H). I will also discuss how the structure of End(Q(H)) completely changes under CH.

Caltech Logic Seminar
Time: Wednesday, December 9, 12:00 – 1:00pm Pacific time (22:00 CET)
Speaker: Jeffrey Bergfalk, University of Vienna
Title: The definable content of (co)homological invariants II: definable cohomology and homotopy classification
Abstract: In this, the second of a three-part series of talks, we describe a “definable Čech cohomology theory” strictly refining its classical counterpart. As applications, we show that, in strong contrast to its classical counterpart, this definable cohomology theory provides complete homotopy invariants for mapping telescopes of dd-tori and of dd-spheres; we also show that it provides an equivariant homotopy classification of maps from mapping telescopes of dd-tori to spheres, a problem raised in the d=1d=1 case by Borsuk and Eilenberg in 1936. These results build on those of the first talk. They entail, for example, an analysis of the phantom maps from a locally compact Polish space X to a polyhedron P; instrumental in that analysis is the definable lim1lim1functor. They entail more generally an analysis of the homotopy relation on the space of maps from X to P, and we will begin by describing a category particularly germane for this analysis. Time permitting, we will conclude with some discussion and application of a related construction, namely that of the definable homotopy groups of a locally compact Polish space X.
This is joint work with Martino Lupini and Aristotelis Panagiotopoulos.
Information: See the seminar webpage.

KGRC Research Seminar
Time:
Thursday, December 10, 15:00 CET
Speaker: Michael Hrušák, UNAM, Mexico City
Title: Invariant Ideal Axiom
Abstract: We shall introduce a consistent set-theoretic axiom which has a profound impact on convergence properties in topological groups. As an application we show that consistently (consequence of IIA) every countable sequential group is either metrizable or kω.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 11 December, 16:30pm CET
Speaker: Assaf Shani, Harvard University
Title: Classification results for countable Archimedean groups
Abstract: We study the isomorphism relation for countable ordered Archimedean groups. We locate its complexity with respect to the hierarchy defined by Hjorth, Kechris, and Louveau, showing in particular that its potential complexity is D(Π03), and it cannot be classified using countable sets of reals as invariants. We obtain analogous results for the bi-embeddability relation, and we consider similar problems for circularly ordered groups and ordered divisible Abelian groups. This is joint work with F. Calderoni, D. Marker, and L. Motto Ros.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Set Theory Seminar
Time: Friday, December 10, 11am New York time (17:00 CET)
Speaker: Dima Sinapova, University of Chicago
Title: Iteration, reflection, and singular cardinals
Abstract: There is an inherent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object. In contrast, failure of SCH is an instance of incompactness.
Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at ℵω+1, and
(2) from large cardinals it is consistent to have the failure of SCH at ℵω.
As these principles are at odds with each other, the natural question is whether we can have both. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at ℵω by interleaving collapses. This is joint work with Alejandro Poveda and Assaf Rinot.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

# Thirteenth Panhellenic Logic Symposium, July 2021

PLS13: THE THIRTEENTH PANHELLENIC LOGIC SYMPOSIUM
July 14-18, 2021, Volos, Greece
Organized by the University of Thessaly
http://panhellenic-logic-symposium.org/

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DISCLAIMER

Our intention is to have a meeting with physical presence, in the spirit of the symposium in all its previous meetings. If this becomes difficult due to the worsening of the pandemic, we will consider other options ranging from an online event to postponing the event to 2022. Any further updates on this front will be posted on the symposium’s webpage.

In any case, we will have a normal Call for Papers procedure; that is, submitted papers will be peer-reviewed and all accepted papers will appear in the electronic (informal) proceedings that we shall post on the event’s webpage.

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IMPORTANT DATES

Deadline for submission:    Friday, March 26, 2021
Final version due:              Wednesday, May 26, 2021

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INVITED TALKS

– Andrew Brooke-Taylor, University of Leeds, UK
– Takayuki Kihara, Nagoya University, Japan
– Julia Knight, University of Notre Dame, USA
– Vassileios Koutavas, Trinity College Dublin, Ireland
– Angus Macintyre, Queen Mary University of London, UK
– Thanases Pheidas, University of Crete, Greece
– Alexandra Silva, University College London, UK
– Linda Brown Westrick, Penn State University, USA

TUTORIALS

– Alex Kavvos, University of Bristol, UK
– Nikos Leonardos, University of Athens, Greece
– Stathis Zachos, National Technical University of Athens, Greece

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SPECIAL SESSIONS

Computer Science:

– Bruno Bauwens, HSE University, Russia
– Juan Garay, Texas A&M University, USA
– Andrew Lewis-Pye, London School of Economics, UK
– Vassilis Zikas, Purdue University, USA & University of Edinburgh, UK

Philosophical Logic:

– Michael Glanzberg, Rutgers University, USA
– Volker Halbach, University of Oxford, UK
– Elia Zardini, University of Lisbon, Portugal & HSE University, Russia

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FIRST CALL FOR PAPERS

The Scientific Committee cordially invites all researchers in the areas of the conference to submit their papers for presentation at PLS13. All submitted papers will be reviewed by the Scientific Committee of the symposium, who will make final decisions on acceptance. Accepted papers will appear in the electronic volume of the event’s (informal) proceedings; the volume will be posted on the event’s webpage. During the actual (in-person) event, each accepted paper will be presented by one of its authors; in case an in-person event cannot happen due to the pandemic, we shall consider other presentation options.

Areas of interest include (but are not limited to):

– Computability Theory
– History and Philosophy of Logic
– Logic in Computer Science
– Model Theory
– Nonclassical and Modal Logics
– Proof Theory
– Set Theory

Papers, in PDF format, should be prepared using the EasyChair class style (easychair.org/publications/for_authors), be written in English, and adhere to a space limit of 6 pages.

Submission is to be done via EasyChair at: https://easychair.org/account/signin?l=SfDov6IqlVTGz0eOMKYlPK#

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POSTER SESSION AND MENTORING SESSION

Graduate students and young researchers are invited to submit a short abstract on work in progress that may not be ready for a regular contributed talk. Those accepted will be able to present their work in poster form in a special poster session. The session will also feature a mentoring component whereby senior researchers will discuss the posters and provide feedback to student participants.

Interested students and young researchers should submit abstracts of no more than one page in PDF form by Friday, June 4, 2021, by sending them to: pls13@softlab.ntua.gr

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GRANTS

Some travel grants will be provided for students and young researchers. Details will be uploaded on the conference webpage as soon as they become available.

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SCIENTIFIC COMMITTEE

– Antonis Achilleos, Reykjavik University
– George Barmpalias, Chinese Academy of Sciences (co-chair)
– Costas Dimitracopoulos, University of Athens
– Pantelis Eleftheriou, University of Konstanz & University of Pisa
– Vassilis Gregoriades, National Technical University of Athens
– Kostas Hatzikiriakou, University of Thessaly
– Antonis Kakas, University of Cyprus
– Alex Kavvos, University of Bristol
– Nikolaos Papaspyrou, National Technical University of Athens
– Thanases Pheidas, University of Crete
– Ana Sokolova, University of Salzburg
– Alexandra Soskova, Sofia University
– Mariya Soskova, University of Wisconsin–Madison
– Yannis Stephanou, University of Athens
– Konstantinos Tsaprounis, University of the Aegean (co-chair)
– Nikos Tzevelekos, Queen Mary University of London
– Niki Vazou, IMDEA Institute
– Stathis Zachos, National Technical University of Athens

ORGANIZING COMMITTEE

– Kostas Hatzikiriakou, University of Thessaly (chair)
– Nikolaos Papaspyrou, National Technical University of Athens
– Vasiliki Papayiannakopoulou, University of Thessaly

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SYMPOSIUM WEBPAGE: http://panhellenic-logic-symposium.org/
E-MAIL: pls13@softlab.ntua.gr

CONTACTS:

– George Barmpalias (barmpalias@gmail.com)
– Konstantinos Tsaprounis (kostas.tsap@gmail.com)
Chairs of the Scientific Committee

– Kostas Hatzikiriakou (kxatzkyr@uth.gr), Chair of the Organizing Committee