Submission date: 29 September 2019

Abstract:

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorčević theory in the more general context of automorphism groups of not necessarily countable structures. One of the main points is a description of the universal ambit as a certain space of types in an expanded language. Using this, we recover various results of Kechris-Pestov-Todorčević, Moore, Ngyuen Van Thé, in the context of automorphism groups of not necessarily countable structures, as well as Zucker.

Mathematics Subject Classification: 03C98, 54H20, 05D10

Keywords and phrases: Group of automorphisms, universal ambit, universal minimal flow, extreme amenability, amenability

Full text arXiv 1909.13285: pdf, ps.