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

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorcevic 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 results of Kechris et al. (Funct Anal 15:106-189, 2005), Moore (Fund Math 220:263-280, 2013), Ngyuen Van The (Fund Math 222: 19-47, 2013), in the context of automorphism groups of not necessarily countable structures, as well as Zucker (Trans Am Math Soc 368, 6715-6740, 2016).