We are pleased to announce that registration for the Winter School in Abstract Analysis 2026, section Set Theory & Topology is now open. The conference will take place between Jan. 31 and Feb. 7 2026, in Hejnice, Czech Republic.

Tutorial speakers for this year are:

• Libor Barto (Charles University)
• Jeffrey Bergfalk (University of Barcelona)
• Paul Larson (Miami University)
• Paul Szeptycki (York University)

Attendees are also invited to contribute research talks.

The early registration conference fee is 15500 CZK (or 640 EUR) and covers all expenses, including the bus from Prague to Hejnice and back. The deadline for payment of the early registration fee is 

        January 11, 2026

After January 11, the conference fee will be 18500 CZK (or 760 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.

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

Caltech Logic Seminar
Time: Wednesday, 5 November, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CET)  
Speaker: François Le Maître, IMB
Title: Rokhlin’s lemma for infinite measure preserving bijections
Abstract: In the probability measure preserving (p.m.p.) setup, a well-known consequence of Rokhlin’s lemma is that any two aperiodic p.m.p. bijections are approximately conjugate, meaning that up to conjugacy, they only differ on sets of arbitrarily small measure. In the infinite measure-preserving (i.m.p.) setup, we will see why this is false and characterize approximate conjugacy for aperiodic i.m.p. bijections. This is joint work with Fabien Hoareau.
Information: See the seminar webpage.

Vienna Logic Colloquium
Time: Thursday, 6 November, 15:00 – 15:50 CET
Speaker: R. Zach, University of Calgary
Title: Semantics of First-order Logic: The Early Years
Abstract: The model and proof theory of classical first-order logic are a staple of introductory logic courses: we have nice proof systems, well-understood notions of models, validity, and consequence, and a proof of completeness. The story of how these were developed in the 1920s, 30s, and even 40s usually consists in simply a list of results and who obtained them when. What happened behind the scenes is much less well known. The talk will fill in some of that back story and show how philosophical, methodological, and practical considerations shaped the development of the conceptual framework and the direction of research in these formative decades. Specifically, I’ll discuss how the work of Hilbert and his students (Behmann, Schönfinkel, Bernays, and Ackermann) on the decision problem in the 1920s led from an almost entirely syntactic approach to logic to the development of first-order semantics that made the completeness theorem possible.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 7 November, 16.00-17.00 CET
Speaker: M. Hoyrup, INRIA
Title: Computable type: an overview
Abstract: A compact metrizable space X has computable type if for every set that is homeomorphic to X, semicomputability is equivalent to computability. This notion was first studied by Joe Miller in 2002, who showed that finite-dimensional spheres all have computable type. It was then developed by Zvonko Iljazović and his co-authors, who showed among many other results that compact manifolds also enjoy this property. I will present recent results on the notion of computable type, obtained in collaboration with Djamel Eddine Amir during his PhD, such as: a simple characterization of 2-dimensional simplicial complexes having computable type, a proof that this property is not preserved by taking binary products.
Information: The event will stream on the Webex platform. Please write to  luca.mottoros [at] unito.it  for the link to the event.

New York Set Theory Seminar
Time: Friday, 7 November, 11.00 New York time (17.00 CET)
Speaker: Emma Palmer, University of Oxford
Title: Tarski’s Revenge
Abstract: Tarski’s nondefinability theorem tells us that we cannot internally define satisfaction in a model via a single first-order formula. But how close can we get to that situation without running into inconsistency? We explore a variety of axioms about satisfaction classes, which, surprisingly, all turn out to be equiconsistent and have only mild consistency strength. For example, from a model of ZFC with an inaccessible cardinal, we can obtain a model of GBC with a definable satisfaction class for an inner model. Indeed, this inner model can even be HOD, or the mantle. Finally, we consider the statement that any set is contained in an inner model with a definable satisfaction class — an axiom we call ‘Tarski’s Revenge’.
Information: Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 7 November, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Paul Szeptycki, York University
Title: The Separable Scarborough-Stone Problem
Abstract: The Scarborough-Stone Problem asks whether the product of any family of sequentially compact spaces is always countably compact. Consistently no, but whether it may have a consistent positive answer remains open. The special case asking whether a separable sequentially compact space has all powers countably compact has, it seems, not been previously studied. We present a consistent counterexample and some related results toward a possible positive solution. This is joint work with César Corral and Alan Dow.
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 7 November, 14.00 New York time (20.00 CET)
Speaker: Roman Kossak, CUNY
Title: Petr Vopěnka’s philosophy of mathematics
Abstract: Petr Vopěnka (1935-2015) was an influential mathematician and deep and original thinker. In the 1970s, he and Petr Hájek developed a system of non-Cantorial set theory, wich was first known the theory of semi-sets, and later became Alternative Set Theory (AST). The primary new concept on which the axioms of AST are based is what Vopěnka called natural infinity. In my talk I will outline some of Vopenka’s thoughts on foundations of mathematics and the role of set theory in it, followed by a discussion of the axioms of AST.
Information: Please see the seminar webpage.

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

Carnegie Mellon University Logic Seminar
Time: Tuesday, 28 October, 4:00 – 5:00pm Pittsburgh time (21:00 – 22:00 CET)
Speaker: Patrick Lutz, University of Michigan
Title: On a question of Day and Marks on a question of Slaman and Steel
Abstract: Martin’s Conjecture is an open problem in computability theory which concerns Turing invariant functions, i.e. functions f such that if x and y are Turing equivalent then so are f(x) and f(y). A well-studied special case of Martin’s Conjecture concerns functions which preserve Turing reducibility, i.e. functions f such that if x is Turing reducible to y then f(x) is Turing reducible to f(y). In the paper “On a question of Slaman and Steel,” Day and Marks raised a question about the existence of functions which are, in a sense, as far from preserving Turing reducibility as possible. In particular, they asked whether there is a function f such that if x is Turing reducible to y then f(x) and f(y) are mutually generic relative to x (which, informally, implies that f(y) is very far from computing f(x)). We will discuss a few partial answers to this question and their connection to Martin’s Conjecture and Borel combinatorics.
Information: See the seminar webpage.

Hebrew University Set Theory Seminar
Time: Wednesday, 29 October, 13:00-15:00 local time (12:00-14:00 CET) 
Speaker: Roy Shalev
Title: Higher Hausdorff gaps
Abstract: We prove that assuming the consistency of a weakly compact cardinal there exists a model of CH in which all -gaps in /countable are Hausdorff.Joint work with Stevo Todorcevic and Borisa Kuzeljevic.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Caltech Logic Seminar
Time: Wednesday, 29 October, 12:00 – 13:00pm Pacific time (20:00 – 21:00 CET)  
Speaker: Riccardo Camerlo, Università di Genova
Title: Isometry groups of Polish ultrametric spaces
Abstract: A characterisation of isometry topological groups of Polish ultrametric spaces is provided. This answers in the context of Polish spaces a problem of Krasner’s. A finer analysis allows also to characterise isometry topological groups of subclasses of Polish ultrametric spaces, providing a solution to questions raised by Gao and Kechris. The groups obtained involve various kinds of generalised wreath products proposed in the literature by Hall, Holland, and Malicki. This is a joint work with A. Marcone and L. Motto Ros.
Information: See the seminar webpage.

Vienna Research Seminar in Set Theory
Time: Thursday, 30 October, 11:30-13:00 CET
Speaker: I. Smythe, University of Winnipeg
Title: The homeomorphism problem for surfaces
Abstract: We show that the homeomorphism problem for arbitrary (noncompact) surfaces is complete for countable structures in the sense of Borel complexity, meaning it is of a maximum complexity among all analytic equivalence relations Borel reducible to the isomorphism problem on some class of countable first-order structures. To do so, we formulate and prove Borel measurable forms of the classical Jordan-Schoenflies and triangulation theorems for surfaces.
This work is joint with Jeffrey Bergfalk. (This talk will be a sequel, with more details, to the Logic Colloquium from Oct 23, 2025.)
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 30 October, 15:00 – 15:50 CET
Speaker: P. Holy, TU Wien
Title: Linear Orderings and Dependent Choice
Abstract: I will talk about a question that was posed on MathOverflow by Joel Hamkins in 2012, namely whether one can have universes of mathematics in which all mathematical objects can be linearly ordered in a uniform way, while this is not possible with respect to wellorders. This question remains open, and I will briefly talk about our attempts at resolving it positively, and then focus on what we think will be a key tool for this — a 1977 paper of David Pincus which shows how to obtain mathematical universes with a uniform linear ordering in which (a generalisation of) the principle of dependent choices holds, however the axiom of choice fails. I will try to provide a rough idea of our modern account of the proofs of Pincus’ theorems.
This is joint work with Jonathan Schilhan.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

New York Set Theory Seminar
Time: Friday, 31 October, 11.00 New York time (16.00 CET)
Speaker: Corey Switzer, University of Vienna
Title: Adding Isomorphisms between Dense Sets of Reals
Abstract: In this talk we will discuss some problems regarding adding linear order isomorphisms between dense sets of reals via forcing. A set of reals A⊆R is called ℵ1-dense just in case it has intersection size ℵ1 with every nonempty open interval. Famously Baumgartner showed in the 70s that consistently all ℵ1-dense sets of reals are order isomorphic, thus establishing the consistency of the natural analogue of Cantor’s categoricity theorem for countable dense linear orders at the uncountable. He later showed the same statement follows from PFA. The statement ‘all ℵ1-dense sets of reals are isomorphic’ is now known as Baumgartner’s axiom and denoted BA. 
Baumgartner’s argument is famously tricky and has several interesting features. Given ℵ1-dense sets A and B he shows that under the continuum hypothesis there is always a ccc partial order for making them isomorphic – but here the CH is important (though it must fail in the final model). Obviously it is therefore natural to ask whether the CH is necessary and, similarly whether BA follows already from MA and not just PFA. Avraham and Shelah showed the answer is ‘no’ to both: they produced a model of MA in which there is an ℵ1-dense set of reals A so that no ccc forcing notion can add an isomorphism between A and its reverse ordering. In the first part of this talk we will strengthen this result by showing that MA is in fact consistent with an ℵ1-dense linear order Aso that any partial order of size ℵ1 which adds an isomorphism between A and its reverse ordering must collapse ℵ1. Thus it is consistent with MA that no such order can even be proper. This part is joint work with Pedro Marun and Saharon Shelah. 
In another direction there is a natural generalization of BA to non-ordered spaces, most notably higher dimensional Euclidean spaces Rn for n>1 as well as compact n-dimensional manifolds. Curiously, in these cases Steprans and Watson showed that the corresponding BA statements do indeed follow from MA so the case of dimension one is unique. In particular BA for Rn with n>1does not imply the one dimensional case. They then conjectured that conversely BA implies its higher dimensional analogues. In the second part of the talk we will introduce some intrigue to this conjecture by showing any ‘reasonable’ way of forcing BA – a very general adjective that includes all known methods – must necessarily force the higher dimensional versions and much more including large fragments of MA.
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 31 October, 14.00 New York time (19.00 CET)
Speaker: Cecelia Higgins, Rutgers University
Title: Complexity of finite Borel asymptotic dimension
Abstract: A Borel graph is hyperfinite if it can be written as a countable increasing union of Borel graphs with finite components. It is a major open problem in descriptive set theory to determine the complexity of the set of hyperfinite Borel graphs. In a recent paper, Conley, Jackson, Marks, Seward, and Tucker-Drob introduce the notion of Borel asymptotic dimension, a definable version of Gromov’s classical notion of asymptotic dimension, which strengthens hyperfiniteness and implies several nice Borel combinatorial properties. We show that the set of locally finite Borel graphs having finite Borel asymptotic dimension is Σ12-complete. This is joint work with Jan Grebik.
Information: Please see the seminar webpage.

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

Carnegie Mellon University Logic Seminar
Time: Tuesday, 21 October, 4:00 – 5:00pm Pittsburgh time (22:00 – 23:00 CEST)
Speaker: Koichi Oyakawa, McGill University
Title: Hyperfiniteness of the boundary action of virtually special groups
Abstract: A Borel equivalence relation on a Polish space is called hyperfinite if it can be approximated by equivalence relations with finite classes. This notion has long been studied in descriptive set theory to measure complexity of Borel equivalence relations. Recently, a lot of research has been done on hyperfiniteness of the orbit equivalence relation on the Gromov boundary induced by various group actions on hyperbolic spaces. In this talk, I will explain my attempt to explore this connection of Borel complexity and geometric group theory for another intensively studied geometric object, which is CAT(0) cube complexes. More precisely, we prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite.
Information: See the seminar webpage.

Hebrew University Set Theory Seminar
Time: Wednesday, 22 October, 13:00-15:00 local time (12:00-14:00 CEST) 
Speaker: Roy Shalev
Title: Higher Hausdorff gaps
Abstract: We prove that assuming the consistency of a weakly compact cardinal there exists a model of CH in which all -gaps in /countable are Hausdorff.Joint work with Stevo Todorcevic and Borisa Kuzeljevic.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria and Inbar Oren for the login information.

Caltech Logic Seminar
Time: Wednesday, 22 October, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)  
Speaker: Tamás Kátay, UCLA
Title: Generic group properties
Abstract: Given a class of groups, say the class of all countably infinite groups, it is natural to ask: what group properties are generic in the sense of Baire category in this class? For this question to make sense, we need a topology. In the case of countably infinite groups, a natural choice is the following: fix N as a common universe and identify every group on N with the group operation that defines it. These group operations form a Polish subspace in NN×N. I will talk about generic group properties in this setting, and, if time permits, I will also say a few words about other settings and generic properties in various classes of topological groups.
Information: See the seminar webpage.

Vienna Research Seminar in Set Theory
Time: Thursday, 23 October, 11:30-13:00 CEST
Speaker: T. Goto, TU Wien
Title: Preservation of the left side of Cichoń’s diagram
Abstract: In the context of countable support iterations, there are two significant preservation theorems. The First Preservation Theorem, due to Shelah, preserves the dominating number of a Fσ relation small. The Second Preservation Theorem, due to Judah–Repický, preserves the bounding number of a Fσ relation small.
It is usual to use The First Preservation Theorem to preserve the right side of Cichoń’s diagram and to use The Second Preservation Theorem to preserve the left side of Cichoń’s diagram. But sometimes The Second Preservation Theorem is inconvenient since it does not help at successor steps. Then we develop methods using The First Preservation Theorem to preserve the left side of Cichoń’s diagram. This method also yields several new constellations of cardinal invariants, which we shall introduce.
This is joint work with Diego Mejía.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 23 October, 15:00 – 15:50 CEST
Speaker: I. Smythe, University of Winnipeg
Title: Manifold classification from the descriptive viewpoint
Abstract: We describe a unified descriptive set-theoretic framework for studying the complexity of classification problems for finite-dimensional manifolds. We establish several precise complexity results, such as for the classification of surfaces up to homeomorphism and for classes of hyperbolic manifolds up to isometry. The latter is intimately connected with the conjugation actions of certain Lie groups on their spaces of discrete subgroups. This work is joint with Jeffrey Bergfalk.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

New York Set Theory Seminar
Time: Friday, 24 October, 11.00 New York time (17.00 CEST)
Speaker: Bartosz Wcisło, University of Gdańsk
Title: Levels of projective determinacy and levels of dependent choice
Abstract: Gitman, Friedman, and Kanovei described a construction of a model of ZF in which countable choice holds and Π12-dependent choice for reals is not satisfied. We modify that construction to obtain a model in which (boldface) Π1n-determinacy holds, but which fails to satisfy (lightface) Π1n+2-DC for reals. In particular, we show that no projective level of determinacy implies full DCR. This is joint work with Sandra Müller.
Information: Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 24 October, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: Jorge Cruz Chapital, University of Toronto
Title: tba
Abstract: tba
Information: Please see the seminar webpage.

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

Leeds Set Theory Seminar
Time: Wednesday, 15 October, 12:00-13:00 local time (13:00-14:00 CEST)
Speaker: Matteo Casarosa, Paris Cite/Bologna
Title: Kurepa families and derived limits
Abstract: Since the 1980s, the derived functors of the inverse limit have been studied through the lens of infinite combinatorics. In particular, when computed on certain inverse systems of abelian groups coming from algebraic topology, vanishing derived limits signal some compactness. Because of this, it is not surprising that combinatorial principles holding in \mathbb{L} imply nonvanishing derived limits for many inverse systems indexed by either the ordinals or spaces of functions. In this talk, we show that the opposite phenomenon occurs for systems indexed by ([\kappa]^{\omega_n}, \subseteq). In fact, the existence of Kurepa families, which is in turn related to square principles, yields vanishing results. This is joint work in progress with Dianthe Basak, Chris Lambie-Hanson, Pedro Marun, Boban Velickovic, and Alessandro Vignati.
Information: Contact Hope Duncan at mmhid@leeds.ac.uk for more information.

Caltech Logic Seminar
Time: Wednesday, 15 October, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)  
Speaker: Andrew Marks, UC Berkeley
Title: Tarski’s circle squaring problem with algebraic translations and few pieces
Abstract: We show that there exists an equidecomposition between a closed disk and a closed square of the same area in R2 by translations with algebraic irrational coordinates. Our proof uses a new method for bounding the discrepancy of product sets in the k-torus using only the Erdős–Turán inequality. This resolves a question of Laczkovich from 1990. We also obtain an improved upper bound on the number of pieces required to square the circle, by proving effective bounds on such discrepancy estimates for translations by certain algebraic irrational numbers. This builds on an idea of Frank Calegari for bounding certain sums of products of fractional parts of algebraic numbers, and some computer assistance. This is joint work with Spencer Unger.
Information: See the seminar webpage.

Vienna Research Seminar in Set Theory
Time: Thursday, 16 October, 11:30-13:00 CEST
Speaker: L. Notaro, Universität Wien
Title: Ladders and Squares
Abstract: Given a positive integer k, a k-ladder is a lower-finite lattice whose elements have at most k lower covers. In 1984, Ditor asked whether for every k there is a k-ladder of cardinality ℵk−1. We show that this question has a positive answer under the axiom of constructibility.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 16 October, 15:00 – 15:50 CEST
Speaker: J. Aguilera, TU Wien
Title: Local Hanf-Tarski numbers
Abstract: We say that a cardinal k is a local Hanf-Tarski number of a logic L if every model M of an L-sentence ϕ of size k can be extended to models of ϕ of arbitrarily large size. In this talk, we present various results concerning local Hanf-Tarski numbers and how they differ from global Hanf-Tarski numbers (for which M is allowed to have size greater than or equal to k) and from classical Hanf numbers.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

New York Set Theory Seminar
Time: Friday, 17 October, 11.00 New York time (17.00 CEST)
Speaker: Calliope Ryan-Smith, University of Leeds
Title: The Axiom of Extendable Choice
Abstract: The Partition Principle (PP) states that if there is a surjection A to B then there is an injection B to A. While this is an immediate consequence of the Axiom of Choice (AC), the question of if PP implies AC is one of the longest-standing open questions in set theory. Partial results regarding this come to us from many sources, including a theorem of Pincus that tells us that if ‘for all ordinals A and all sets B, if there is a surjection B to A then there is an injection A to B’ implies AC for well-orderable families of sets. We shall dissect this and related results, looking into the history of the structure of the cardinals in choiceless models and following the throughline to modern research on eccentric sets and the structure of cardinals as a partial order.
Information: Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 17 October, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: Ari Brodsky, Shamoon College of Engineering
Title: tba
Abstract: tba
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 17 October, 14.00 New York time (20.00 CEST)
Speaker: Hans Schoutens, CUNY
Title: Can categories categorize the theories of model-theory?
Abstract: I want to argue that when knowing the model-theory of categories, you kind of know the model-theory of any structure. As the ? at the end of the title suggests, some of this is still speculative. 
It is easy to see a category as a first-order structure in the two-sorted language (for objects and morphisms) of categories; a little less to do this foundationally correct (I have given a talk a way back in which I ignored these issues, but I will correct this in the talk, although not mentioning them in this abstract). Now, to any theory T in some first-order language L, we can associate a theory in the language of categories, cat(T), which reflects this theory: the models of cat(T) are isomorphic (as categories) with subcategories of the category Mod(T) of models of T. In fact, any category that is elementary equivalent with Mod(T) is a sub-model of the latter.
This translation from T into cat(T)—from an arbitrary signature to a fixed one—is still mysterious, and as of now, I only know a very few concrete cases. A key role seems to be played by the theory FO, consisting of all sentences in the language of categories which hold in each category of L-structures, for all possible languages L. But I do not even know yet a full axiomatization of FO.
Information: Please see the seminar webpage.

The call for nominations for the Hausdorff Medal 2026 from 1 October with deadline 1 December is available here:

Click to access Hausdorff%20Medal%202026%20Text.pdf

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

Vienna Research Seminar in Set Theory
Time: Thursday, 9 October, 11:30-13:00 CEST
Speaker: N. Chapman, TU Wien
Title: Ranked Forcing and the Structure of Borel Hierarchies
Abstract: The structural study of the Borel hierarchy on topological spaces is a foundational goal of descriptive set theory. By an early result of the field, we know that there exist universal sets at each level α<ω1 of the Borel hierarchy on the Baire space ωω, hence the order of this hierarchy, i.e. the first ordinal α at which every Borel set has been generated, attains the maximal possible value of ω1. However, there are other subspaces of ωω where this hierarchy is shorter; take for example any countable space, on which every Borel subset must be Σ02.
The topic of this talk is a framework for the surgical alteration of the complexity of the Borel hierarchy on subspaces of ωω, pioneered by A. Miller. We will discuss Miller’s notion of α-forcing, which allows for either collapsing or increasing the length of the Borel hierarchy, as well as the proof ideas behind some preservation theorems necessary to do so. In the second part of the talk, we will delve into recent developments in this area, such as an extension of the framework to the field of generalized descriptive set theory of an uncountable cardinal κ=κ<κ or the study of the λ-Borel subsets of κκ for λ>κ, with a particular emphasis on the case λ=ω1 and κ=ω. We will give several examples of models constructed using this method in both the classical case of ω and the generalized case of an uncountable κ. Lastly, we will discuss some limitations of the technique and directions for future work.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Vienna Logic Colloquium
Time: Thursday, 9 October, 15:00 – 15:50 CEST
Speaker: R. Honzik, Charles U Prague
Title: Compactness in mathematics
Abstract: We discuss some well-known compactness principles for uncountable structures of small regular sizes ωn for 2≤n<ω, ℵω+1, ℵω2+1, etc.), consistent from weakly compact (the size-restricted versions) or strongly compact or supercompact cardinals (the unrestricted versions). For the exposition, we divide the principles into logical principles, which are related to cofinal branches in trees and more general structures (various tree properties), and mathematical principles, which directly postulate compactness for structures like groups, graphs, or topological spaces (for instance, countable chromatic and color compactness of graphs, compactness of abelian groups, Δ-reflection, Fodor-type reflection principle, and Rado’s Conjecture).
We also focus on indestructibility, or preservation, of these principles in forcing extensions. While preservation adds a degree of robustness to such principles, it also limits their provable consequences. For example, some well-known mathematical problems such as Suslin Hypothesis, Whitehead’s Conjecture, Kaplansky’s Conjecture, and the categoricity of ω1-dense subsets of the reals (Baumgartner’s Axiom), are independent from some of the strongest forms of compactness at ω2. This is a refined version of Solovay’s theorem that large cardinals are preserved by small forcings and hence cannot decide many natural problems in mathematics. Additionally, we observe that Rado’s Conjecture plus 2ω=ω2 is consistent with the negative solutions, i.e. as they hold in V=L, of some of these conjectures (Suslin’s, Whitehead’s, and Baumgartner’s axiom), verifying that they hold in suitable Mitchell models.
Finally, we comment on whether the compactness principles under discussion are good candidates for axioms. We consider their consequences and the existence or non-existence of convincing unifications (such as Martin’s Maximum or Rado’s Conjecture). This part is a modest follow-up to the articles by Foreman “Generic large cardinals: new axioms for mathematics?” and Feferman et al. “Does mathematics need new axioms?”.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

New York Set Theory Seminar
Time: Friday, 10 October, 11.00 New York time (17.00 CEST)
Speaker: Dan Hathaway, University of Vermont
Title: On Absoluteness Between V and HOD
Abstract: We put together Woodin’s Σ21 basis theorem of AD+ and Vopěnka’s theorem to conclude the following: If there is a proper class of Woodin cardinals, then every (Σ21)uB statement that is true in V is true in HOD. Moreover, this is true even if we allow a certain parameter. We then show that stronger absoluteness cannot be implied by any large cardinal axiom consistent with the axiom V = Ultimate L.
Information: Please see the seminar webpage.

New York Logic Workshop
Time: Friday, 10 October, 14.00 New York time (20.00 CEST)
Speaker: Philip Scowcroft, Wesleyan University
Title: Injective simple dimension groups
Abstract: A dimension group is a partially ordered Abelian group whose partial order is isolated and directed and has the Riesz interpolation property. A dimension group is simple just in case it has no nontrivial ideals, ideals being directed convex subgroups. By concentrating on the behavior of positive formulas in simple dimension groups, this talk will reveal a well-behaved part of their model theory.
Information: Please see the seminar webpage.

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

Vienna Research Seminar in Set Theory
Time: Thursday, 30 September, 15:00 CEST
Speaker: Y. Li, University of Amsterdam
Title: Ramsey property and madness
Abstract: We give an expository introduction of Schrittesser and Törnquist’s result that under some weak choice principle, all sets having the Ramsey property implies that there is no infinite maximal almost disjoint family (MAD) family. In particular, this gives a proof that there is no MAD family in the Solovay Model. We also discuss how their result localizes in the projective hierarchy.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Carnegie Mellon University Logic Seminar
Time: Tuesday, 30 September, 4:00 – 5:00pm Pittsburgh time (22:00 – 23:00 CEST)
Speaker: Jiaming Zhang, Carnegie Mellon University
Title: A Forcing Perspective on the Covering Lemma
Abstract: This talk reviews the covering lemma, one of the most fundamental results in inner model theory. Briefly, the covering lemma offers a criterion for measuring the proximity between the core model K and the set-theoretic universe V. Specifically, if a K-cardinal alpha>omega_2 is regular in K but singular in V, then alpha must be a measurable cardinal in V. This theorem was initially established by Mitchell under a stronger hypothesis and later refined in a 2023 paper by Schimmerling and Mitchell. We proved that under some additional conditions, V contains a Prikry generic of alpha, and we can define a maximal Prikry sequence of alpha. This is a joint work with Prof. Schimmerling.
Information: See the seminar webpage.

Vienna Logic Colloquium
Time: Thursday, 2 October, 15:00 – 15:50 CEST
Speaker: P. Marimon, TU Wien
Title: Minimal operations above permutation groups
Abstract: We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a classical theorem of Rosenberg says that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen. Building on these results, we answer some questions of Bodirsky related to constraint satisfaction problems (CSPs), a natural class of computational problems.
This is joint work with Michael Pinsker.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

New York Set Theory Seminar
Time: Friday, 3 October, 11.00 New York time (17.00 CEST)
Speaker: Eyal Kaplan, University of California, Berkeley
Title: The number of normal measures, revisited
Abstract: A central question in the theory of large cardinals was whether the existence of a model of ZFC with exactly two normal measures follows from the consistency of ZFC with a measurable cardinal. This was answered positively by a landmark theorem of Friedman and Magidor, whose proof masterfully combined advanced techniques in the theory of large cardinals, including generalized Sacks forcing, forcing over canonical inner models, coding posets, and nonstationary support iterations.
In this talk, we present a new and simpler proof of the Friedman-Magidor theorem. A notable feature of our approach is that it avoids any use of inner model theory, making it applicable in the presence of very large cardinals that are beyond the current reach of the inner model program. If time permits, we will also discuss additional applications of the technique: the construction of ZFC models with several normal measures but a single normal ultrapower; a nontrivial model of the weak Ultrapower Axiom from the optimal large cardinal assumption; and a generalization of the Friedman–Magidor theorem to extenders.
Information: Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 3 October, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: Andy Zucker, University of Waterloo
Title: tba
Abstract: tba
Information: Please see the seminar webpage.

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

Carnegie Mellon University Logic Seminar
Time: Tuesday, 23 September, 4:00 – 5:00pm Pittsburgh time (22:00 – 23:00 CEST)
Speaker: Nathaniel Bannister, Carnegie Mellon University
Title: tba
Abstract: tba
Information: See the seminar webpage.

Vienna Research Seminar in Set Theory
Time: Thursday, 25 September, 11:30-13:00 CEST
Speaker: L. Gardiner, University of Cambridge
Title: Colouring copies of the rationals
Abstract: We demonstrate some results in the theory of infinite-exponent partition relations on linear orders and show that a certain relation of this type implies the failure of the choice principle KWP1. We then answer a question of Fatalini about an analogous result in the setting of graphs.
This is joint work with Thilo Weinert and Jonathan Schilhan.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.

Ronald Jensen was born in Virginia in the US in 1936. After having completed a BA in economics in New York in 1959, he decided to move to Europe and become a logician. He finished his Ph.D. with G. Hasenjaeger at the University of Bonn in 1964 with a thesis on subsystems of arithmetic, and he did his Habilitation at Bonn in 1967 on levels of the constructible hierarchy.

Jensen developed the fine structure theory all by himself, isolated diamond, square, and other combinatorial principles which he showed to hold in L, and he used his machinery to present his Covering Lemma for L as “Marginalia to a Theorem of Silver.” He designed various forcing techniques, one of the most sophisticated ones being the coding into a real apparatus. In joint work with T. Dodd he built the first core model, an enterprise which was later pursued by W. Mitchell, J. Steel, and others. He later worked on the theory of larger core models. He also isolated the notions of “subproper” and “subcomplete” forcings and variants thereof, and he produced his own iteration theory for them. He designed “L-forcing.” In his last years, he worked on a book on the core model below one Woodin cardinal.

Jensen held positions at the Rockefeller University, at UC Berkeley, at the University of Bonn, the University of Oslo, the University of Freiburg, the University of Oxford, and the Humboldt University of Berlin, from which he retired in 2001.

Jensen was the first Gödel lecturer of the Association for Symbolic Logic in 1990. In 2001, he gave the Tarski lectures at UC Berkeley. In 2003, he reveived the Steele price. In 2015, the European Set Theory Society awarded him and J. Steel the Hausdorff Medal for their joint paper “K without the measurable.”

Jensen was an honorary president of the European Set Theory Society since 2016. 

On September 16, 2025 Ronald Jensen passed away. He left us his life’s work mostly in the form of thousands of pages of handwritten notes. A lot of current-day set theory consists in generalizing concepts and arguments which go back to Jensen. Set theory lost one of its giants.



- Ralf Schindler