Christopher Eagle: Baire Category and the Omitting Types Theorem

Place: BA6183

Date: July 21 , 2017 (13:30-15:00)

Speaker: Christopher Eagle

Title: Baire Category and the Omitting Types Theorem

Abstract: It is well-known that the Omitting Types Theorem from model theory can be proved by topological means, and the central ingredient of that proof is the Baire Category Theorem.  The goal of this talk is to consider the extent to which the Omitting Types Theorem is equivalent to the Baire Category Theorem.  To do so, we will describe a topological framework (based on work of Robin Knight) that generalizes the classical type spaces from model theory.   Many classical logics (including first-order, infinitary, and continuous logics) fit into this general setting, and conversely we will show that each instance of the general framework yields a model-theoretic logic.  We then distinguish several version of the Omitting Types Theorem these logics may have, based on Baire Category properties of the underlying topological spaces.  All of these properties are equivalent for first-order logic, but are distinct in the general setting.  This is joint work with Frank Tall.

Dorottya Sziráki: Open colorings on generalized Baire spaces

Thursday, July 20, 2017,  10:30–12.00

Main Lecture Hall , Alfréd Rényi Institute of Mathematics

Abstract: We study the uncountable version of a natural variant of the Open Coloring Axiom. More concretely, suppose that $\kappa$ is an uncountable cardinal such that $\kappa^{<\kappa}=\kappa$ and X is a subset of the generalized Baire space $\kappa^\kappa$ (the space of functions from $\kappa$ to $\kappa$ equipped with the bounded topology). Let OCA*(X) denote the following statement: for every partition of $[X]^2$ as the union of an open set R and a closed set S, either X is a union of $\kappa$ many S-homogeneous sets, or there exists a $\kappa$-perfect R-homogeneous set. We show that after Lévy-collapsing an inaccessible $\lambda>\kappa$ to $\kappa^+$, OCA*(X) holds for all $\kappa$-analytic subsets X of $\kappa^\kappa$. Furthermore, the Silver dichotomy for ${\Sigma}^0_2(\kappa)$ equivalence relations on $\kappa$-analytic subsets also holds in this model. Thus, both of the above statements are equiconsistent with the existence of an inaccessible $\lambda>\kappa$. We also examine games related to the above partition properties.

Yann Pequignot: Sigma^1_2 sets and countable Borel chromatic numbers

Friday, July 21th, 2017, 10.00-12.00

Aula S, Palazzo Campana, Università di Torino

Speaker: Yann Pequignot (University of California, Los Angeles)

Title: Sigma^1_2 sets and countable Borel chromatic numbers

Abstract:

Analytic sets enjoy a classical representation theorem based on wellfounded relations. I will explain a similar representation theorem for Sigma^1_2 sets due to Marcone. This can be used to answer negatively the primary outstanding question from (Kechris, Solecki and Todorcevic; 1999): the shift graph is not minimal among the graphs of Borel functions which have infinite Borel chromatic number.

Workshop on Computability Theory and Foundations of Mathematics, Singapore, September 8-12, 2017


 

CALL FOR PRESENTATION


Workshop on Computability Theory and Foundations of Mathematics
(National University of Singapore, 8 – 12 September 2017)

http://www2.ims.nus.edu.sg/Programs/017wcom/index.php

Abstracts of talks should be submitted via email to imsbox1@nus.edu.sg with the subject line: CTFM2017 submission.

The length of abstract is limited to 2 pages including references. The authors are recommended to prepare their abstracts in the following IMS format:
Tex file: http://ims.nus.edu.sg/files/IMSAbstractTemplate.tex
PDF example: http://ims.nus.edu.sg/files/IMSAbstractTemplate.pdf

Submission deadline: September 1, 2017


This workshop is the seventh in the Computability Theory and Foundations of Mathematics (CTFM) series. CTFM aims to provide a forum for computability theory and logical foundations of mathematics. The topics include, but are not limited to, Computability / Recursion Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Algorithmic Randomness and Computational Complexity.

CTFM began as a “Workshop on Proof Theory and Computability Theory” and held its first meeting in Japan. Previous venues were Matsushima (2008, 2009), Inawashiro (2010), Sendai (2011), Tokyo (2012). The series assumed the name “Computability and Foundations of Mathematics” at the 2013 meeting which was hosted in Tokyo. CTFM 2017 will be the first time a meeting in the series is held outside Japan.

The previous meetings attracted not only researchers in Japan but also many from around the world. In particular, since 2013, logicians from Singapore have had frequent scientific exchanges with their Japanese counterpart through the platform of the CTFM meetings.

The first day and the last day of the 2017 workshop will focus on classical recursion theory, and computable structures as well as reverse mathematics. The activities are held jointly with the program Aspect of Computation. The other two days will focus on topics in set theory and the foundations of mathematics.


Invited Speakers

Joerg Brendle (Kobe University, Japan)
Satoru Kuroda (Gunma Prefectural Women’s University, Japan)
Ludovic Patey (The University of California, Berkeley, USA)
Toshimichi Usuba (Waseda University, Japan)
Thomas Zeugmann (Hokkaido University, Japan)
Hao Zhaokuan (Fudan University, China)


Program Committee

Dilip Raghavan (National University of Singapore)
Stephen Simpson (Pennsylvania State University)
Frank Stephan (National University of Singapore)
Kazuyuki Tanaka (Tohoku University) (Chair)
Yue Yang (National University of Singapore)
Keita Yokoyama (Japan Advanced Institute of Science and Technology)


Organizing Committee

Chi Tat Chong (National University of Singapore)
Kazuyuki Tanaka (Tohoku University)
Guohua Wu (Nanyang Technological University)
Yue Yang (National University of Singapore)
Keita Yokoyama (Japan Advanced Institute of Science and Technology)


 

Ultrafilters, Ramsey Theory and Dynamics, Villeurbanne, November 20-24, 2017

Ultrafilters, Ramsey Theory and Dynamics

20-24 Nov 2017 Villeurbanne (France)

Description

This week-long event, scheduled between November 20 and November 24, 2017 at the University of Lyon 1, is a combined school and workshop focusing primarily on the rich interactions between ultrafilters, topological dynamics and ergodic theory and applications to Ramsey theory. This event is part of the thematic semester “Graphs, Groups and Dynamics”.

Mini-Course Lecturers:

  • Vitaly Bergelson :
  • Neil Hindman : Central Sets
  • Imre Leader : Ramsey Theory

Invited speakers:

  • Ben Barber
  • Dana Bartosova
  • Mathias Beiglböck
  • Natasha Dobrinen
  • Daniel Glasscock
  • John Johnson
  • Jordi Lopez Abad
  • Joel Moreira
  • Florian Richter
  • Julian Sahasrabudhe
  • Dona Strauss
  • Konstantinos Tyros
  • Andrew Zucker

Local organizing committee

Francois Hennecart (Université Jean-Monnet)

Johannes Kellendonk (Université Lyon 1)

Lionel Nguyen Van Thé (Université d’Aix-Marseille)

Carine Sevestre (LABEX MiLyon)

Stéphan Thomassé (ENS de Lyon)

Luca Q. Zamboni (Université Lyon 1)

Scientific Committee

-Vitaly Bergelson (Ohio State University, USA)

-Neil Hindman (Howard University, USA)

-Imre Leader (University of Cambridge, UK)

Stevo Todorčević (University of Toronto, CA)

Dániel T. Soukup: Uncountable strongly surjective linear orders

Thursday, July 13, 2017,  10:30

Seminar Room, Alfréd Rényi Institute of Mathematics

Abstract: A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We review various results on the existence and non-existence of uncountable strongly surjective linear orders answering questions of Camerlo, Carroy and Marcone. In particular, $\diamondsuit^+$ implies the existence of a lexicographically ordered Suslin-tree which is strongly surjective and minimal; every strongly surjective linear order must be an Aronszajn type under $2^{\aleph_0} <2^{\aleph_1}$ or in the Cohen and other canonical models (where $2^{\aleph_0}=2^{\aleph_1}$); finally, we show that it is consistent with CH that there are no uncountable strongly surjective linear orders at all. Further details and open problems can be found in https://arxiv.org/abs/1706.10171

Set Theoretic Methods in Topology and Analysis, Będlewo, September 3-9, 2017

Set Theoretic Methods in Topology and Analysis

03.09.2017 – 09.09.2017 | Będlewo

Aims and scope:

  • The purpose of the conference is to bring together well-known specialists and young researchers working in set theory, topology, and their applications in other branches of mathematics, including algebra and functional analysis.

Invited speakers:

  • Uri Abraham, Ben-Gurion University of the Negev, Beer Sheva, Israel
  • Antonio Avilés, University of Murcia, Spain
  • Angelo Bella, University of Catania, Italy
  • Lev Bukovský, Pavol Jozef Safarik University in Košice, Slovakia
  • Alan Dow, University of North Carolina at Charlotte, USA
  • David H. Fremlin, University of Essex, UK
  • Sakaé Fuchino, Kobe University, Japan
  • István Juhász, Hungarian Academy of Sciences, Hungary
  • Piotr Koszmider, Polish Academy of Sciences, Poland
  • Menachem Magidor, Hebrew University of Jerusalem, Israel
  • Ol’ga Sipacheva, M. V. Lomonosov Moscow State University, Russia
  • Mikhail Tkachenko, Metropolitan Autonomous University, Mexico
  • Lyubomyr Zdomskyy, Kurt Gödel Research Center for Mathematical Logic, Austria

 

 

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Jindra Zapletal: Quotient forcings defined from group actions

Dear all,

The seminar meets on Wednesday July 12th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jindra Zapletal will talk about quotient forcings defined from group
actions.

Best,
David

Winter School, Jan 27 – Feb 3, 2018

The Winter School in Abstract Analysis, section Set Theory & Topology will take place between Jan 27th and Feb 3rd 2018 in Hejnice, Czech Republic.

Tutorial speakers for the Winter School 2018 are:

Leandro Aurichi
Joel David Hamkins
Jordi Lopez-Abad
Itay Neeman

The registration will open in October 2017, conference fee is expected to be 350 EUR and covers all expenses including the bus from Prague to Hejnice and back. Accommodation will be in double rooms.

Registration deadline — December 31st, 2017

To get more information about the conference please visit the web page

www.winterschool.eu

If you have any questions please do not hesitate to contact us.

We hope to see you in January,

David Chodounský, Jan Starý and Jonathan Verner

Saeed Ghasemi: Scattered C*-algebras

Place: Bahen Centre (Room 6183)

Date: July 7th, 2017 (13:30-15:00)

Speaker: Saeed Ghasemi, Polish Academy of Sciences

Title: Scattered C*-algebras

Abstract: By the Gelfand duality, the theory of C*-algebras can be
regarded as “non-commutative topology”. In a joint work with Piotr
Koszmider at IMPAN, we investigated the non-commutative analogues of
the scattered spaces, parallel to the classical research in
set-theoretic topology. The so called scattered C*-algebras, despite
being around in the literature, have not been subject to the tools
from set-theoretic topology. The techniques and constructions of
compact, Hausdorff scattered spaces, or equivalently (by the Stone
duality) superatomic Boolean algebras, have already led to many
fundamental results in the theory of Banach spaces of the form C(K),
or more generally Asplund spaces. In fact scattered C*-algebras were
introduced as C*-algebras which are Asplund as Banach spaces. I will
introduce the notion of the Cantor-Bendixson derivatives for these
C*-algebras, and present some of the basic properties of such
algebras. I will also show how it can be used to construct C*-algebras
with exotic properties, which are non-commutative versions of
well-known scattered spaces. In particular, the constructions of
non-commutative Psi-spaces and thin tall spaces lead to new
discoveries about the preservation of the “stability” for
non-separable C*-algebras.