## Model Theory Seminar on Monday 11/3/2014 and 11/17/2014

Sebastien Vasey will continue talking on his infinitely long paper,
delivering parts 4 and 5:

———————————————————
Model Theory Seminar

Sebastien Vasey

Carnegie Mellon
Title: Infinitary stability theory, part IV

Abstract: In 1990, Makkai and Shelah studied the class of models of an
$L_{\kappa, \omega}$ sentence, where $\kappa$ is strongly compact. Among
many other results, they showed that Galois types (a purely semantic
notion of types) and syntactic types conveyed the same information. In
particular, Galois types are determined by their restrictions to sets of
size less than $\kappa$. This last property was later isolated by
Grossberg and VanDieren and called tameness. In this talk, I will show
that tameness already implies that Galois types are (in some sense)
syntactic, thus generalizing Makkai and Shelah’s result. I will give
several applications to the stability theory of tame abstract elementary
classes.

Date: Monday, November 3, 2014
Time: 5:00 – 6:30 PM
Location: Wean 8220

——————————————————–

Model Theory Seminar

Sebastien Vasey

Carnegie Mellon
Title: Infinitary stability theory, part V

Abstract: In 1990, Makkai and Shelah studied the class of models of an
$L_{\kappa, \omega}$ sentence, where $\kappa$ is strongly compact. Among
many other results, they showed that Galois types (a purely semantic
notion of types) and syntactic types conveyed the same information. In
particular, Galois types are determined by their restrictions to sets of
size less than $\kappa$. This last property was later isolated by
Grossberg and VanDieren and called tameness. In this talk, I will show
that tameness already implies that Galois types are (in some sense)
syntactic, thus generalizing Makkai and Shelah’s result. I will give
several applications to the stability theory of tame abstract elementary
classes.

Date: Monday, November 17, 2014
Time: 5:00 – 6:30 PM
Location: Wean 8220

## 8th Young Set Theory Workshop, October 25-30, 2015

The 8th Young Set Theory Workshop will take place October 25-30 2015, at the Israel Institute of Advanced Studies in Jerusalem.

The aims of the “Young Set Theory Workshops” are to bring together young researchers in the domain of set theory and give them the opportunity to learn from each other and from experts in a friendly environment. A long-term objective of this series of workshops is to create and maintain a network of young set theorists and senior researchers, so as to establish working contacts and help disseminate knowledge in the field.

There will be four minicourses, five invited talks by young set theorists, and a few more invited 1-hour talks by senior set theorists.

### MINICOURSES:

 Alexander S. Kechris (Caltech) [tentative] Péter Komjáth (Eötvös) Menachem Magidor (HUJI) W. Hugh Woodin (Harvard)

## Jeremy Avigad: Uniform distribution and algorithmic randomness II

Mathematical logic seminar – October 28, 2014
Time: 12:30 – 13:30

Room: Wean Hall 8220

Department of Philosophy
CMU

Title: Uniform distribution and algorithmic randomness II

Abstract:

A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct
integers, then, for almost every real number x, the sequence (a_n x) is
uniformly distributed modulo one. In particular, for almost every x in the unit
interval, the sequence (a_n x) is uniformly distributed modulo one for every
*computable* sequence (a_n) of distinct integers. Call such an x UD random.

Every Schnorr random real is UD random, but there are Kurtz random reals that
are not UD random. On the other hand, Weyl’s theorem still holds relative to a
particular effectively closed null set, so there are UD random reals that are
not Kurtz random.

In these talks, I will prove Weyl’s theorem and provide the relevant background
from algorithmetic randomness, and then discuss the results above.

## Chong Chi Tat: Lowness of reals in higher randomness

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 29 October 2014, 17:00 hrs

Room: S17#04-04, Department of Mathematics, NUS

Speaker: Chong Chi Tat

Title: Lowness of reals in higher randomness

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract: This talk will discuss the problem of the existence
of nontrivial reals which are low for various notions of higher
randomness, reporting on the works of several authors.

## Jordi Lopez Abad: Ramsey properties of embeddings between finite dimensional normed spaces

Date:  24-October-2014

Time: 13:30- 15:00

Place:  Fields Institute, Room 210

Title: Ramsey properties of embeddings between finite dimensional normed  spaces.

Abstract:  Given $d\le m$, let $E_{m,n}$ be the set of all $m\times d$ matrices $(a_{i,j})$ such that

(a) $\sum_{j=1}^d |a_{i,j}|\le 1$ for every $1\le i\le m$.

(b) $\max_{i=1}^m |a_{i,j}|=1$ for every $1\le j\le d$.

These matrices  correspond to the linear isometric embeddings from the normed space $\ell_\infty^d:=(\mathbb{R}^d,\| \cdot \|_\infty)$ into $\ell_\infty^d$, in their unit bases.

We will discuss and give (hints of) a proof of the following new approximate Ramsey result:

For every integers $d$, $m$ and $r$ and every $\varepsilon>0$ there exists $n$ such that for every coloring of $E_{d,n}$ into $r$-many colors there is $A\in E_{m,n}$ and a color $i<r$ such that
\begin{equation*}
A \cdot  E_{d,m}\subseteq (c^{-1}(i))_\varepsilon.
\end{equation*}
Its proof uses the Graham-Rothschild Theorem on partitions of finite sets.
We extend this result, first for embeddings between \emph{polyhedral} normed spaces, and finally for arbitrary finite dimensional normed spaces to get the following:

For every finite dimensional normed spaces $E$ and $F$, every $\theta>1$ and $\varepsilon>0$, and every integer $r$, there is some $n$ such that for every coloring of $\mathrm{Emb}_{\theta^2}(F,\ell_\infty^n)$ into $r$-many colors there is $T\in \mathrm{Emb}_{\theta}(G,\ell_\infty^n)$ and some color $i<r$ such that $T\circ \mathrm{Emb}_\theta(F,G)\subseteq (c^{-1}(i))_{\theta^2-1+\varepsilon}$.

As a consequence, we obtain that the group of linear isometries of the Gurarij space is extremely amenable. A similar result for positive isometric embeddings gives that the universal minimal flow of the group of affine homeomorphisms of the Poulsen simplex is the Poulsen simplex itself.

This a joint work (in progress) with Dana Bartosova (University of Sao Paulo) and Brice Mbombo (University of Sao Paulo)

## Marcin Michalski: Luzin and Sierpiński sets, some nonmeasurable subsets of the plane

Tuesday, October 21, 2014, 17.05
D1-215, Politechnika Wroclawska

Speaker: Marcin Michalski (Wroclaw University of Technology)

Title: Luzin and Sierpiński sets, some nonmeasurable subsets of the plane

Abstract:

## Double session at Fields Institute (D. Bartosova and A. Rinot)

Place: Fields Institute, Room 210

Date: 17-October- 2014

Time: 12:30-15:00

Speaker 1 (from 12:30 to 13:30): Dana Bartosova
Title: Finite Gowers’ Theorem and the Lelek fan
Abstract: The Lelek fan is a unique non-degenrate subcontinuum of the Cantor fan with a dense set of endpoints. We denote by $G$ the group of homeomorphisms of the Lelek fan with the compact-open topology. Studying the dynamics of $G$, we generalize finite Gowers’ Theorem to a variety of operations and show how it applies to our original problem. This is joint work with Aleksandra Kwiatkowska.
___________________________________________________________
Speaker 2 (from 13:30 to 15:00): Assaf Rinot
Title: Productivity of higher chain condition
Abstract: We shall survey the history of the study of the productivity of the k-cc in partial orders, topological spaces, and Boolean algebras. We shall address a conjecture that tries to characterize such a productivity in Ramsey-type language. For this, a new oscillation function for successor cardinals, and a new characteristic function for walks on ordinals will be proposed and investigated.

## Sarka Stejskalova: Laver diamond, PFA from a supercompact cardinal

Wednesday, October 15, 2014, 11:00
Prague – CTS

Speaker: Sarka Stejskalova

Title: Laver diamond, PFA from a supercompact cardinal

## Winter School 2015

We are pleased to announce that the registration for the Winter School in Abstract Analysis, section Set Theory & Topology is now open. The conference will take place between Jan 31st and Feb 7th 2015 in Hejnice, Czech Republic.

Tutorial speakers for this year are:

Claude Laflamme
David Milovich
Justin T. Moore
Andrzej Roslanowski

The conference fee is 300 EUR and covers all expenses including the bus from Prague to Hejnice and back. Accommodation will be in double rooms.

We have a limited amount of money to support students and researchers without other sources of funding.

Dec 11th, 2014 fee waiver application deadline

www.winterschool.eu

Hope to see you in January

David Chodounsky, Jan Stary and Jonathan Verner

## Wu Guohua: Nonhemimaximal sets and degrees

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 15 October 2014, 17:00 hrs

Room: S17#04-04, Department of Mathematics, NUS

Speaker: Wu Guohua

Title: Nonhemimaximal sets and degrees

Abstract: In this talk, I will present a recent work with Mustafa and
Yamaleev on the Turing degrees of nonhemimaximal sets, proving that
the nonhemimaximal degrees are nowhere dense in the low2 c.e.
degrees. This answers a question of Downey and Stob.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html