# Model Theory Seminar

### School of Mathematics, University of Leeds

All the seminars will be in MALL 2 and will be on Tuesdays at 2pm. We will usually meet before the seminar at about 1.40pm in the common room for tea and coffee.

The seminar is organised by Will Anscombe.

### Autumn Term 2013

Week 11, Tuesday 10th December
Ningyuan Yao
Definable Amenability of NIP Theories

In NIP theories, a global type which is finitely satisfiable in small submodel is "Borel definable" over such submodel. If we assume NIP, and consider a definable group $G(x)$ which has fsg, that is, there exists a global type $p(x)\vdash G(x)$ such that every left translation of $p(x)$ is finitely satisfiable in a small submodel. Then, by Borel definability of $p(x)$, for each definable subset $X$ of $G$, $X/G^{00}$ should be a Borel subset of the compact group $G/G^{00}$, and the Haar measure of $X/G^{00}$ gives $X$ a left invariant measure. Moreover, $X$ has positive measure iff $X$ is finitely satisfiable in every small submodel, such $G$ is called definable amenable group.