## Boris Zilber: Structural approximation.

HUJI Logic Seminar

The next meeting of the Logic Seminar will take place in Wednesday, 07/12, 16:00 – 18:00, in Ross Building 70.
Please forward this mail to anyone who might be interested in this talk (or in the seminar).

Structural approximation.

Speaker: Boris Zilber
Abstract. In the framework of positive model theory I will give (recall) a definition of “structural approximation”  which is used in my paper on model-theoretic interpretation of quantum mechanics. I will then present some general theory as well as a few examples.

## Misha Gavrilovich: Elementary topology via finite topological spaces

BGU Seminar in Logic, Set Theory and Topology

Time: Tuesday, December 5th, 12:30-13:45.
Place: Seminar room -101, Math building 58.
Speaker: Misha Gavrilovich.

Title: Elementary topology via finite topological spaces

Abstract:
We observe that several elementary definitions in point-set topology
can be reformulated in terms of finite topological spaces
and elementary category theory. This includes compactness
of Hausdorff spaces, being connected, discrete, the separation axioms.

Though elementary, these observations raise a few open questions.
For example, I was not able to prove that this reformulation of
compactness gives the correct answer for non-Hausdorff spaces,
or whether implications between various topological properties
can also be proved entirely in terms of finite topological spaces,

## Franklin Tall: On the sigma-compactness of definable Menger spaces

Place: Fields Institute (Room 210)

Date: December 2, 2016 (13:30-15:00)

Speaker: Franklin Tall, University of Toronto

Title: On the sigma-compactness of definable Menger spaces

Abstract:  In a previous seminar, we saw that an inaccessible sufficed for the consistency of “every projective Menger set of reals is sigma-compact”. The inaccessible is in fact necessary.

## Andy Zucker: Ramsey degrees big and small II

Mathematical logic seminar – November 29 2016
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Andy Zucker
Department of Mathematical Sciences
CMU

Title:     Ramsey degrees big and small II

Abstract:

We will consider various aspects of structural Ramsey theory in a countable first-order structure, leading to an investigation of several notions of largeness. For ultrahomogeneous (i.e. Fraisse) structures, the Ramsey theoretic properties of the structure and the dynamical properties of the automorphism group are closely related. This talk should serve as an introduction to the Kechris-Pestov-Todorčević correspondence while also discussing directions for new research.

## Andrés Villaveces: Around the Small Index Property on quasiminimal classes

BGU Seminar in Logic, Set Theory and Topology, 29/11/16, 12:30-13:45, building 58, room -101
AND
HUJI Logic Seminar,  30/11/16, 16:00-18:00, Ross Building, room 70

Speaker: Andrés Villaveces (Universidad Nacional, Bogotá).Title: Around the Small Index Property on quasiminimal classes

Abstract:
In the study of the connection between automorphism groups of models and the models themselves (or their theories, or their bi-interpretability class), the Small Index Property (SIP) has played a central role. The work of Hodges, Lascar, Shelah and Rubin among others has established in many cases when a model of a first order theory T has the Small Index Property.With Ghadernezhad, we have studied this property for more general homogeneous classes. We have isolated properties of closure notions that allow to prove the SIP for some non-elementary cases, including Zilber’s pseudo-exponentiation and other examples.I will present a panorama of these results, including our more recent generalizations of the Lascar-Shelah proof of SIP for uncountable structures. This last part is joint work with Zaniar Ghadernezhad.

## Juris Steprans: Automorphisms of $P(\omega)/fin$

Place: Fields Institute (Room 210)

Date: November 25th, 2016 (13:30-15:00)

Speaker: Juris Steprans, York University

Title: Automorphisms of $P(\omega)/fin$

Abstract:

The question of whether all automorphisms of $P(\kappa)/fin$ are trivial has been settled in the following cases:

– For $\kappa =\omega$ by Rudin and Shelah
– For $\kappa$ between $\omega_2$ and the first inaccessible by work of Larson & McKenney and Shelah and me.

However the second result hinges on the question for automorphisms of $P(\omega_1)/fin$. I will discuss a resolution to this question stemming from recent work of Shelah and me.

## Artur Bartoszewicz: On the sets of subsums of series

Tuesday, November 29, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Artur Bartoszewicz (Łódź University of Technology)

Title: On the sets of subsums of series

Abstract:

The first observations connected with sets of subsums of series (s.c. achievement sets) belong to Kakeya and are over 100 years old. In my lecture I want to present the story of the studies of the problem and the results obtained by my cooperators and me quite recently. These results concern the series generating Cantorvals, connections between the achievement sets of series and the atractors of affine IFS’s and achievement sets of conditionally convergent series in the plane.

## Matthew Foreman: Applications of Descriptive Set Theory in Ergodic Theory

Attached are slides of a series of talks given by Matt Foreman at the UCI seminar.

## Assaf Rinot: Hindman’s theorem and uncountable Abelian groups

Mathematics Colloquium, Bar-Ilan University

Sunday, 27/Nov/2016, 14:00-15:00

Speaker: Assaf Rinot

Title: Hindman’s theorem and uncountable Abelian groups

Abstract. In the early 1970’s, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell.

In this talk, we shall study generalizations of this statement. Among other things, we shall present a negative partition relation for the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah.

This is joint work with D.J. Fernandez Breton from the University of Michigan

## Alex Usvyatsov: Model theoretic techniques in Banach space geometry

HUJI Logic seminar

The next meeting of the Logic Seminar will take place in Wednesday, 23/11/16, at Ross 70, between 16:00 and 18:00.
Speaker:  Alex Usvyatsov
Model theoretic techniques in Banach space geometry

Abstract: I will discuss a model theoretic approach to certain basic questions in Banach space geometry, and some interesting questions. In this talk, I will only use soft model theory and explain the meaning of all the relevant properties (such as stability and definability) in this context.