Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

Abstract: It is a well-known fact, that the greatest ambit for a topological group $G$ is the Samuel compactification of $G$ with respect to the right uniformity on $G.$ We apply the original destription by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using Fra\"iss\'e theory and Ramsey theory. This work generalizes some of the known results about countable structures.