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.
Linear orders Automorphism groups Countable categoricity Extreme amenability Fraïssé classes Ramsey property
Nguyen Van Thé, L.: Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups. Eur. J. Comb. 30(4), 934–945 (2009)MathSciNetMATHCrossRefGoogle Scholar