Automorphism Groups of Countably Categorical Linear Orders are Extremely Amenable

TL;DR

This paper proves that automorphism groups of countably categorical linear orders are extremely amenable and uses this to establish a structural Ramsey theorem for specific finite ordered structures.

Contribution

It establishes the extreme amenability of automorphism groups for a class of linear orders and derives a new structural Ramsey theorem using advanced methods.

Findings

Automorphism groups of countably categorical linear orders are extremely amenable.

A structural Ramsey theorem for finite ordered structures with partial equivalence relations.

Application of Kechris, Pestov, and Todorcevic's methods to these structures.

Abstract

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite ordered structures with finitely many partial equivalence relations with convex classes.