The weekly announcements will be moved to the new website http://settheory.eu soon.

Carnegie Mellon University Logic Seminar
Time: Tuesday, 16 September, 4:00 – 5:00pm Pittsburgh time (22:00 – 23:00 CEST)
Speaker: Long Qian, Carnegie Mellon University
Title: An axiomatic approach to Ordinary Differential Equations
Abstract: Classically, differential equations are often reasoned about by computing their solutions, and their properties are deduced from numerical approximations. This talk will focus on an alternative approach that provides an axiomatic treatment of ODEs, where properties are deduced from the ODEs directly based on a small set of axioms in the logical system of differential dynamic logic. Practically, this provides a framework for (formal) theorem proving for ODEs, yielding machine-checkable proofs. An introduction to this logic will be provided, with a focus on recent results concerning completeness fragments of this logic.
Information: See the seminar webpage.

Hebrew University Set Theory Seminar
Time: Wednesday, 17 September, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Leeds Set Theory Seminar
Time: Wednesday, 17 September, 13:00-14:00 local time (14:00-15:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Hope Duncan at mmhid@leeds.ac.uk for more information.

Toronto Set Theory Seminar
Time: Friday, 19 September, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: Tom Benhamou, Rutgers University
Title: On the Point and Depth Spectrum
Abstract: The point and depth spectrum of a directed set are adjoined sets of regular cardinals that can be viewed as a measure of cofinal complexity. The first was studied in the 50s and 60s by Tukey, Schmidt and Isbell, and more recently Gartside-Mamatelashvili and Gilton studied certain relations between the point spectrum and PCF theory. Here we use PCF theory to study the supremum of the point spectrum and present several results regarding the point and depth spectrum of an ultrafilter. In the second part of the talk we present a Hechler-like result, producing ultrafilter base of prescribed isomorphism type. We then use these results to obtain new consistency results- answering several questions about the spectrums and in the realm of generalized cardinal characteristics.
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 19 September, 14.00 New York time (20.00 CEST)
Speaker: James Walsh, New York University
Title: A theory satisfying a strong version of Tennenbaum’s theorem
Abstract: Tennenbaum’s theorem states that no non-standard model of PA is computable. Hence, no unsound extension of PA has computable models. Pakhomov recently showed that this consequence of Tennenbaum’s theorem is fragile; it depends on the signature in which PA is presented. In particular, there is a theory T such that (i) T is definitionally equivalent to PA (this is a strong form of bi-interpretability) and (ii) every consistent r.e. extension of T has a computable model. Pakhomov’s techniques yield analogous results for ZF and other canonical systems. He asked whether there is a consistent, r.e. theory T such that no theory which is definitionally equivalent to T has a computable model. We answer this question with an ad hoc construction. This is joint work with Patrick Lutz.
Information: Please see the seminar webpage.

The weekly announcements will be moved to the new website http://settheory.eu soon.

This week’s special event: Sixth European Set Theory Colloquium, Wednesday, 11 September, 17:00-18:30 CEST.

Carnegie Mellon University Logic Seminar
Time: Tuesday, 9 September, 4:00 – 5:00pm Pittsburgh time (22:00 – 23:00 CEST)
Speaker: Hannah Hoganson, University of Maryland
Title: How hard is it to determine if graphs are proper homotopy equivalent?
Abstract: Motivated by the study of mapping class groups, we discuss the proper homotopy equivalence relation for locally finite graphs. We show that the Borel complexity of this equivalence relation is bireducible with the homeomorphism relation on closed subsets of the Cantor set, so by work of Camerlo and Gao, it is Borel complete. On the other hand, we will see that there is a generic equivalence class. We construct Polish spaces of locally finite graphs in such a way that we can extend these results to the homeomorphism relation for noncompact surfaces with pants decompositions. This is joint work with Jenna Zomback.
Information: See the seminar webpage.

Hebrew University Set Theory Seminar
Time: Wednesday, 10 September, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Sixth European Set Theory Colloquium
Time: Wednesday, 11 September, 17:00-18:30 CEST
Panelists: Juliette Kennedy, University of Helsinki; Chris Lambie-Hanson, Czech Academy of Sciences; Philipp Lücke, University of Hamburg; Farmer Schlutzenberg, Technical University of Vienna
Information: This colloquium will take place in person and on zoom at: https://tuwien.zoom.us/j/61571518141?pwd=V0WDh1U0S2Gz1qguPvkI5H215EITKD.1, Meeting-ID: 615 7151 8141; Password: 66E4R4qs. It will be moderated by Sandra Müller. It is organised by Sandra Müller, Philipp Schlicht and Zoltan Vidnianszky.

New York Set Theory Seminar
Time: Friday, 12 September, 11.00-12.30 New York time (17.00-18.30 CEST)
Speaker: Rahman Mohammadpour, Institute of Mathematics of Polish Academy of Sciences
Title: Specializing Triples
Abstract: I will talk about weak embeddability and the universality number of the class of Aronszajn trees, with a focus on the role of specializing triples. 
The notion of a specializing triple was introduced by Džamonja and Shelah in their strong negative solution to an old problem on the existence of a universal (with respect to weak embeddability) wide Aronszajn tree under Martin’s axiom. Their proof has two stages: first, they reprove a theorem of Todorčević showing that under MAω1 there is no universal Aronszajn tree, and then they show that every wide Aronszajn tree weakly embeds into an Aronszajn tree. The second stage involves a rather complicated ccc forcing. However, already in the first stage, they introduce a new technique: the notion of a specializing triple, and prove that for each Aronszajn tree T, there is a ccc forcing adding another Aronszajn tree T∗ together with a specializing function on T∗⊗T such that (T∗,T,c) is a specializing triple. In particular, this shows that T∗ does not weakly embed into T. 
I will explain how a slight but careful modification of this definition makes it possible to accommodate wide trees directly, yielding a more streamlined proof of Džamonja and Shelah’s result. More precisely, for every κ-wide Aronszajn tree T, there is a ccc forcing adding an Aronszajn tree T∗ and a function c such that (T∗,T,c) is what I call a left specializing triple. From this, one quickly recovers Džamonja-Shelah’s theorem: under Martin’s axiom, every class of trees of height ω1 and size less than the continuum but with no cofinal branches either is not universal for Aronszajn trees, or has universality number equal to the continuum. 
Finally, I will indicate how the modified definition can also be used to show that this consequence of Martin’s axiom is consistent with the existence of a nonspecial Aronszajn tree.
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 12 September, 14.00 New York time (20.00 CEST)
Speaker: Gunter Fuchs, CUNY
Title: Strong reflection, saturation and diagonal reflection. A study of a triangle relationship
Abstract: There is a natural way to formulate fragments of Todorcevic’s strong reflection principle (SRP) which are associated to forcing classes more restrictive than the class of all stationary set preserving forcing notions. The fragment associated to the subcomplete forcings (SC-SRP), while retaining many crucial consequences of SRP, is compatible with CH, and even Jensen’s Diamond Principle. In particular, the saturation of the nonstationary ideal, a celebrated consequence of SRP, does not follow from its subcomplete fragment. In fact, adding CH to SC-SRP results in a principle which outright contradicts the saturation of the nonstationary ideal. A specific form of diagonal reflection of stationary sets of ordinal was used by Paul Larson to separate SRP from Martin’s Maximum: that form of diagonal reflection follows from MM, but not from SRP. The surprising initial observation is that it does follow from SC-SRP + CH. The key reason for this is that SC-SRP + CH implies the nonsaturation of the nonstationary ideal. Thus, an apparent weakness of SC-SRP + CH turns out to be a strength in this context.
I will introduce the concepts involved and present some further results along these lines. The picture that emerges is that in the context of SC-SRP, saturation and diagonal reflection work against each other.
This is joint work with Hiroshi Sakai.
Information: Please see the seminar webpage.

The Sixth European Set Theory Colloquium will take place at 17:00-18:30 central European summer time (CEST) on Wednesday, 10 September 2025 in hybrid form at the Young Set Theory Workhop at the Technical University of Vienna.

The panelists are:

• Juliette Kennedy, University of Helsinki
• Chris Lambie-Hanson, Institute of Mathematics of the Polish Academy of Sciences
• Philipp Lücke, University of Hamburg
• Farmer Schlutzenberg, Technical University of Vienna
  
  The colloquium will be moderated by Sandra Müller.
  
  The zoom information for this colloquium is:
  https://tuwien.zoom.us/j/61571518141?pwd=V0WDh1U0S2Gz1qguPvkI5H215EITKD.1
  Meeting-ID: 615 7151 8141; Password: 66E4R4qs

There have recently been emails purportedly sent by Vera Fischer in connection with activities of the ESTS, trying to make contact with members of the set theory community and asking you to reply. The goal of these emails is likely to eventually obtain private information from you or trick you into payments if you reply. 

Please 
– do not give any personal information to the senders of such emails
– carefully check the sender of such emails and report the emails as spam with your email service
– we’re happy if you can forward us a copy of such spam emails to european.set.theory@gmail.com, or email us there if you are in doubt

All emails from the ESTS to its members, including membership fee reminders, are sent exclusively from european.set.theory@gmail.com. We will never ask you for personal information. The only information we keep about members are name, email address and whether you are a student. 

Best wishes, the board of the ESTS 

This is a reminder of the Early Career Award 2025 of the European Set Theory Society. This prestigious award recognizes outstanding scientific achievements in set theory by researchers in the early stages of their careers. The award includes the European Set Theory Society Early Career Award certificate and five years of complimentary ESTS membership.

Eligibility
Candidates must have received their PhD no earlier than 15 June 2018. Extensions to this time limit will be considered in cases of extenuating circumstances, such as parental leave or other significant career interruptions.

Award Criteria
The award will be granted in recognition of significant scientific contributions to the field of set theory that extend beyond the results of the candidate’s Ph.D. thesis. The selection will be made by a designated committee. The award is highly competitive and intended to reflect exceptional research accomplishments.

Application Procedure
Candidates should submit the following materials:
—  A cover letter briefly outlining their research achievements and career trajectory
—  A curriculum vitae, including a list of publications In addition, candidates must arrange for two reference letters, focusing on their post-Ph.D. scientific contributions, to be sent to the email address below by the same deadline.

Submission Address
All materials should be submitted via email to: <european.set.theory@gmail.com>

Deadline
All application materials must be received by July 15, 2025.

— The Board of the European Set Theory Society

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Hebrew University Set Theory Seminar
Time: Wednesday, 2 July, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: Yair Hayut
Title: Dense ideals on small cardinals
Abstract: In the previous lectures we proved that consistently (relative to large cardinals), for every regular cardinal kappa, there is an ideal I on kappa+ such that P(kappa+)/I has a dense subset isomorphic to Col(kappa,kappa+).
In this talk we will discuss some consequences of this consistency result. We will prove the Woodin-Foreman Boolean transfer theorem (in the easier special case of dense ideals), showing how to derive -dense ideals on  in this model. Then, we will derive consequences related to some compactness of the chromatic number from graphs which follows from the existence of those dense ideals.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Leeds Set Theory Seminar
Time: Wednesday, 2 July, 13:00-14:00 local time (14:00-15:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Hope Duncan at mmhid@leeds.ac.uk for more information.

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Hebrew University Set Theory Seminar
Time: Wednesday, 25 June, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Leeds Set Theory Seminar
Time: Wednesday, 25 June, 13:00-14:00 local time (14:00-15:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Hope Duncan at mmhid@leeds.ac.uk for more information.

Vienna Research Seminar in Set Theory
Time: Thursday, 26 June, 11:30-13:00 CEST
Speaker: C. Gallart Rodriguez, Universität Wien
Title: Forcing with symmetric side conditions of models of two types
Abstract: In this talk, I will give an introduction to the technique of forcing with side conditions and present some of the results obtained using the recently introduced symmetric matrices of models of two types.
The idea of adding systems of countable models as side conditions has been exploited extensively by Todorčević to build forcing notions that preserve cardinals and obtain consequences of forcing axioms at the level of the first uncountable cardinal.
The addition of models of a second type in recent work of Neeman, Asperó-Mota, Veličković, and others has proven to be very effective in pushing these results one cardinal higher, but most importantly, it has opened the door to obtaining consistent high analogs of classical strong forcing axioms.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 26 June, 15:00 – 15:50 CEST
Speaker: Zoltan Vidnyánszky, Eötvös Loránd University, Budapest
Title: Two complexity results
Abstract: The characterization of hyperfinite equivalence relations is a major open problem of descriptive set theory. A similarly notorious open problem is whether every hyper-hyperfinite equivalence relation is hyperfinite.
In this talk, I will show that, perhaps surprisingly, a negative answer to the latter implies a negative answer to the former. I will also discuss a recent development connecting Borel amenability to complexity.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

The European Set Theory Society is pleased to announce the Early Career Award 2025. This prestigious award recognizes outstanding scientific achievements in set theory by researchers in the early stages of their careers. The award includes the European Set Theory Society Early Career Award certificate and five years of complimentary ESTS membership.

Eligibility
Candidates must have received their PhD no earlier than 15 June 2018. Extensions to this time limit will be considered in cases of extenuating circumstances, such as parental leave or other significant career interruptions.

Award Criteria
The award will be granted in recognition of significant scientific contributions to the field of set theory that extend beyond the results of the candidate’s Ph.D. thesis. The selection will be made by a designated committee. The award is highly competitive and intended to reflect exceptional research accomplishments.

Application Procedure
Candidates should submit the following materials:
—  A cover letter briefly outlining their research achievements and career trajectory
—  A curriculum vitae, including a list of publications In addition, candidates must arrange for two reference letters, focusing on their post-Ph.D. scientific contributions, to be sent to the email address below by the same deadline.

Submission Address
All materials should be submitted via email to: <european.set.theory@gmail.com>

Deadline
All application materials must be received by July 15, 2025.

— The Board of the European Set Theory Society

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Hebrew University Set Theory Seminar
Time: Wednesday, 18 June, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: Yair Hayut
Title: Dense ideals
Abstract: In this series of talks, I will present joint work with Monroe Eskew. The main result of our work is the relative consistency of the existence of dense ideals on all successors of regular cardinals simultaneously: namely, it is consistent that there is a -dense normal ideal on  for every cardinal  which is a successor of a regular cardinal. In particular, we show that it is consistent that for every <img height="9" width="41" src="https://ci3.googleusercontent.com/meips/ADKq_NZOHZq-dV0JH17ip8eCCwmfxEM_HnT0zFnUp4Xbm74bQpXHpKQBsCLQJXujWvfLktgbUZ4lxZwAyC32xdJdzqvc8bqig9xChtBgJLXbWANfP4jV4oPrCp1ciJvcGtr3Pj7BrA=s0-d-e1-ft#https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=n%3C%5Comega&quot; alt="n, there exists an -dense ideal on , thus extending Foreman’s result for .
Beginning in the 1980s, Foreman proposed the philosophy of generic large cardinal axioms — a parallel hierarchy to the traditional large cardinal axioms. Unlike the classical axioms, these generic versions aim to settle set-theoretic questions about small cardinals, such as the Continuum Hypothesis. Just as large cardinals are characterized via combinatorial objects like measures, generic large cardinal axioms correspond to the existence of ideals with certain properties. One way to measure the strength of such an axiom is by how small the Boolean algebra of positive sets mod the ideal can be: the smaller, the better.
We begin by presenting a variant of Laver’s consistency proof for the existence of a saturated ideal. If time permits, we will also show that Martin’s Maximum implies the saturation of the non-stationary ideal on .
Later in the series, we will describe the classical construction of a dense ideal on  from an almost-huge cardinal. The main part of our work involves a new forcing notion — a variant of a construction introduced by Shioya. We iterate this forcing and, starting from a huge cardinal, produce a dense ideal on the successor of any regular cardinal.
Information: This talk will take place exclusively via zoom. Please contact Inbar Oren in advance for the login information.

Leeds Set Theory Seminar
Time: Wednesday, 18 June, 13:00-14:00 local time (14:00-15:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Contact Hope Duncan at mmhid@leeds.ac.uk for more information.

There is an open call for 10 positions in the PhD program in Mathematics at the University of Torino, Italy; the deadline is June 16^th. See below for technical details. Currently, the logic group in Turin consists of 4 PhD students, 2 post-docs, and 6 professors (see here for more information). Our research is centered around set theory, descriptive set theory, model theory, and their connections with category theory, computability, and group theory. Given the number of open positions for this year, the chances that at least one of them will be assigned to a student interested in logic are reasonably high. Do not hesitate to contact us if you have any questions, and feel free to forward this message to anyone who might be interested.

Details:

Here you can find the call and information on how to apply.

Deadline: June 16^th.

There are 10 positions with scholarship, with one reserved for candidates with a foreign master degree.

See here for a description of the 10 positions, some of which involve a joint supervision with a foreign partner. See also this link for a list of research topics with corresponding possible supervisors.

The interviews for the selection of candidates will take place in July, and can be carried out online. The outcome of the selection will be published at the beginning of August; admitted candidates have 7 days to accept the position.

Candidates can obtain their Master degree by October 31^st, 2025 (and not by the expiry date of the call). 

The starting date of the PhD program is November 1^st, 2025.