A Short Note on Extreme Amenability of Automorphism Groups of ω-Categorical Structures

Abstract

In this short note we would like to point out a straighforward corllary of the recent result of Dorais, Gubkin, McDonald and Rivera that the automorphism group of every ω-categorical linear order is extremely amenable: it follows that an oligomorphic permutation group G is contained in an extremely amenable permutation group if and only if it preserves a linear order.