## 5th European Set Theory Conference, August 24 – 28, 2015

The 5th European Set Theory Conference (5ESTC) is the fifth meeting in a series of biannual meetings coordinated by the European Set Theory Society. Earlier meetings were held in Bedlewo (1ESTC, July 2007 and 2ESTC, July 2009), Edinburgh (3ESTC, July 2011) and Mon St. Benet (4ESTC, July 2013).

As part of 5ESTC, we are celebrating the 70th birthday of Adrian Mathias during the Mathias Day (Thursday). The programme consists of a tutorial, the Mathias Day, plenary lectures, invited (parallel lectures) and contributed talks.

The programme committee consists of Joan Bagaria (chair), Mirna Dzamonja, Benedikt Löwe, Ralf Schindler, and Philip Welch.

Tutorial:

Mathias Day speakers:

Plenary speakers:

Invited speakers:

## Wadge theory and automata, January 28, 2015

The logic group in Turin is pleased to announce a one-day workshop on “Wadge theory and automata”. Wadge theory is an area of descriptive set theory dealing with the classification of subsets of reals in terms of their topological complexity. It has strong connections with automata theory, in particular when it comes to classifying omega-regular languages that can be recognized by different types of automata.

The workshop will take place on January 28th, 2015 at Palazzo Campana in the center of Turin, and will consist of four talks.

## Program

10:00 to 10:50 – Jacques Duparc (Lausanne)

#### Reductions by relatively continuous relations on the space of finite and infinite sequences of integers

11:00 to 11:20 – Coffee Break
11:20 to 12:10 – Alessandro Facchini (Warsaw)

#### The Index and Borel/Wadge Definability Problems for Regular Languages of Infinite Trees

12:20 to 14:00 – Lunch Break
14:00 to 14:50 – Victor Selivanov (Novosibirsk)

#### Extending the Wagner hierarchy to k-partitions

15:00 to 15:20 – Coffee Break
15:20 to 16:10 – Olivier Finkel (Paris)

#### Logic, Complexity, and Infinite Computations

16:20 to 16:40 – Discussion session

Everyone is cordially invited to attend. Please forward this announcement to anyone who could be interested in this event.

We will make available modest travel awards to graduate or recent Ph.D. students so that they may attend the workshop. To be considered for a travel award, please send a letter of application by e-mail at the address luca.mottoros@unito.it. The application letter should be brief (preferably one page) and should include: (1) your name; (2) your home institution; (3) your thesis supervisor’s name; (4) a one-paragraph description of your studies and work in logic, and a paragraph indicating why it is important to attend the meeting; (5) your estimate of the travel expenses you will incur. The deadline for the submission of a letter of application is 09.01.2014.

We hope to see you soon in Turin!

Alessandro Andretta, Raphaël Carroy, Luca Motto Ros and Matteo Viale

## David Chodounsky: Y-properness of Laver and Miller forcing

Wednesday, December 17, 2014, 11:00
Prague – IM AS CR, Zitna 25, konirna (front building, ground floor)

Speaker: David Chodounsky

Title: Y-properness of Laver and Miller forcing

## Matt Foreman: Measure preserving diffeomorphisms of the torus are not classifiable

Friday Set Theory Seminar (HUJI)

We shall meet Friday (December 19) in the Hebrew University math
department building, Room 110, at 10 am.

Speaker: Matt Foreman (UCI)

Title: Measure preserving diffeomorphisms of the torus are not classifiable.

Abstract: In joint work with B Weiss, we show that the isomorphism relation for diffeomorphisms of the torus is complete analytic. Moreover it lies above every S^\infty action in the hierarchy of equivalence relations under Borel reducibility.

See you there!

## Grzegorz Plebanek: About a particular measure on the square

Tuesday, December 16, 2014, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Grzegorz Plebanek (University of Wroclaw)

Title: About a particular measure on the square

Abstract:

Assuming the existence of Sierpiński set we construct a measure on some sigma-field of subsets of the square which is perfect but not compact. This construction in 2001 answered Fremlin’s question. We will describe open problems connected to this field.

## Michal Machura: The P-hierarchy of ultrafilters

Infinite Combinatorics Seminar (BIU)

14/December/2014, 10:15-12:00,
Room 201, Building 216, Bar-Ilan University

Speaker: Michal Machura (BIU)

Title: The P-hierarchy of ultrafilters

Abstract: We shall present the P-hierarchy of ultrafilters, that was posed by Andrzej Starosolski.
The P-hierarchy of ultrafilters is one of many ways to classify ultrafilters on natural numbers and it is composed of $\aleph_1$  disjoint classes $P_{\alpha}$ where $\alpha$ is ordinal number $<\omega_1$. The class $P_{1}$ is just a class of principal ultrafilters. The class $P_{2}$ is composed of  P-points,  which were defined by Rudin in order to prove non-homogenity of the remainder of Cech-Stone compactification of natural numbers. Next, in higher classes of P-hierarchy, one can find ultrafilters with more and more complicated structures.
In this talk, we will disscuss relations between classes $P_{\alpha}$ of P-hierarchy and other special types of ultrafilters like: Baumgartner’s I-ultrafilters, thin ultrafilters, summable ultrafilters, and van der Waerden ultrafilters.

## Ryszard Frankiewicz: Around the Gitik-Shelah theorem

Forcing seminar (Tel Aviv University)

December 9th 2014, 9-11

Speaker: Ryszard Frankiewicz

Title: Around the Gitik-Shelah theorem

## Juliette Kennedy: Change the logic, change the meaning? Inner models and extended logics.

Friday Set Theory Seminar (HUJI)

We shall meet Friday (December 12) in the Hebrew University math
department building, at 10 am.

Speaker: Juliette Kennedy (Helsinki)

Title: Change the logic, change the meaning? Inner models and extended logics.

Abstract: In his 1946 Princeton Bicentennial Lecture Gödel suggested the problem of finding a notion of definability for set theory which is “formalism free” in a sense similar to the notion of computable function — a notion which is very robust with respect to its various associated formalisms. One way to interpret this suggestion is to consider standard notions of definability in set theory, which are usually built over first order logic, and change the underlying logic. We show that constructibility is not very sensitive to the underlying logic, and the same goes for hereditary ordinal definability (or HOD). Some interesting intermediate models are discussed. This is joint work with Menachem Magidor and Jouko Väänänen.

See you there!

## Chris Lambie-Hanson: Bounded Stationary Reflection

Students Set Theory Seminar (HUJI)

We shall meet Wednesday (December 10) in the Hebrew University (in Ross 70), 14:45-16:00.

Speaker: Chris Lambie-Hanson

Title: Bounded Stationary Reflection

Abstract: Eisworth, motivated in part by his work on square-bracket partition relations, asked whether it must be the case that if mu is a singular cardinal and every stationary subset of mu^+ reflects, then every stationary subset of mu^+ reflects at an ordinal of arbitrarily high cofinality below mu. We will give some background motivation, sketch a proof answering this question in the negative, and discuss various variations on Eisworth’s question.

## Andrés Caicedo: Co-analytic uniformization

Wednesday, December 10 from 3 to 4pm
Room: Math 226
Speaker: Andrés Caicedo (BSU)
Title: Co-analytic uniformization

Abstract: It is an easy consequence of the axiom of choice that if X is an arbitrary set and R is a binary relation on X (a subset of $X^2$) then R admits a uniformization, that is, there is a function f whose domain is $\{x \in X : \text{there is a } y \in X \text{ with } x R y\}$ and such that for all x in its domain, x R f(x).

If X is the set of reals, and R is a reasonably definable relation, one might expect that the existence of such a function f can actually be established without using the axiom of choice.

We sketch a classical result independently due to Novikov and Kondo showing that this is indeed the case if R is Borel (and even if it is “slightly” more complicated than Borel).