Topological dynamics of unordered Ramsey structures

2014/01/30 by Müller, Moritz, Pongrácz, András
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1401.7766

Abstract

In this paper we investigate the connections between Ramsey properties of Fraisse classes K and the universal minimal flow M(G_K) of the automorphism group G_K of their Fraisse limits. As an extension of a result of Kechris, Pestov and Todorcevic we show that if the class K has finite Ramsey degree for embeddings, then this degree equals the size of M(G_K). We give a partial answer to a question of Angel, Kechris and Lyons showing that if K is a relational Ramsey class and G_K is amenable, then M(G_K) admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.

Related

• Big Ramsey degrees and topological dynamics
• Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
• A Fraïssé theory for partial orders of a fixed finite dimension
• Twenty years of Nešetřil's classification programme of Ramsey classes
• Amenability and Unique Ergodicity of Automorphism Groups of Fraïssé Structures