On the topological dynamics of automorphism groups; a model-theoretic perspective

Abstract

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todor\v{c}evi\'{c} 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-Todor\v{c}evi\'{c}, Moore, Ngyuen Van Th\'{e}, in the context of automorphism groups of not necessarily countable structures, as well as Zucker.