Krzysztof Krupinski: Amenable theories

The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory.

Abstract:
I will introduce the notion of an amenable theory as a natural counterpart of the notion of a definably amenable group. Roughly speaking, amenability means that there are invariant (under the action of the group of automporphism of a sufficiently saturated model), Borel, probability measures on various types spaces. I will discuss several equivalent definitions and give some examples. Then I will discuss the result that each amenable theory is G­compact. This is a part of my recent paper (still in preparation) with Udi Hrushovski and Anand Pillay.