Extremely amenable groups via continuous logic

TL;DR

This paper characterizes the extreme amenability of Polish groups using continuous logic and Fraïssé theory, extending previous results to a broader class of groups.

Contribution

It provides a new Fraïssé-theoretic characterization of extreme amenability for Polish groups within continuous logic, generalizing earlier theorems.

Findings

Extended the characterization of extreme amenability to all Polish groups.

Connected continuous logic with topological group properties.

Generalized Kechris-Pestov-Todorcevic theorem to a broader setting.

Abstract

We establish a characterization of extreme amenability of any Polish group in Fra\"iss\'e-theoretic terms in the setting of continuous logic, mirroring a theorem due to Kechris, Pestov and Todorcevic for closed subgroups of the permutation group of an infinite countable set.