Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

TL;DR

This paper computes the universal minimal flows for automorphism groups of uncountable structures using Samuel's original description, extending known results from countable to uncountable cases via Fraïssé and Ramsey theory.

Contribution

It introduces a method to determine universal minimal flows for uncountable structures' automorphism groups, generalizing previous countable results.

Findings

Provides a simple computation method for uncountable structures' automorphism groups

Extends known results from countable to uncountable structures

Utilizes Samuel's original description with Fraïssé and Ramsey theory

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.