The seminar meets on Tuesdays, 12:30-13:45, in Math -101

## Fall 2016 meetings

Date
Title
Speaker
Abstract
Nov 8 Tight stationarity and pcf theory - part one Bill Chen (BGU)

I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcf-theoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.

Nov 15 Tight stationarity and pcf theory - part two Bill Chen (BGU)

I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcf-theoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.

Nov 22 Pseudo-finite groups and centralizers Daniel Palacín (HUJI)

In this talk I will prove that any pseudo-finite group contains an infinite abelian subgroup. Additionally, I shall also discuss some other results concerning pseudo-finite groups and centralizers.

This is joint work with Nadja Hempel.

Nov 29 Around the Small Index Property on quasiminimal classes Andrés Villaveces (Universidad Nacional, Bogotá)

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.