Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

Is there a theory of measures for simple theories?  A Keisler measure is a finitely additive probability measure on definable subsets.  Although measures in simple theories arise naturally in examples (e.g. pseudo-finite simple structures) and there are some promising general tools (e.g. Keisler randomization), very little is known generally about the possible behavior of Keisler measures in simple theories.  We will describe some results that show that the world of measures in simple theories is more complicated than expected.  In particular, we will describe a generic expansion of SL_2(C) with a generic paradoxical decomposition, showing that there are groups in simple theories that are not definably amenable.  This is joint work with Artem Chernikov, Ehud Hrushovski, Alex Kruckman, Krzysztof Krupinski, and Anand Pillay. 

Groups And Measures In Simple Theories