Topological dynamics of automorphism group of countably categorical structures

TL;DR

This paper investigates the topological dynamics of automorphism groups of countably categorical structures, demonstrating that omega-stable omega-categorical structures have metrizable universal minimal flows and exploring their amenability.

Contribution

It establishes the metrizability of universal minimal flows for automorphism groups of omega-stable omega-categorical structures and examines their amenability properties.

Findings

Automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows.

The paper studies the amenability of these automorphism groups.

Results are foundational for understanding the dynamics of automorphism groups in model theory.

Abstract

We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study amenability of these groups. This is a draft of a paper which will be extended by some other results.