Topological dynamics of unordered Ramsey structures
Volume 230 / 2015
Fundamenta Mathematicae 230 (2015), 77-98
MSC: Primary 05C55; Secondary 37B05, 03C15.
DOI: 10.4064/fm230-1-3
Abstract
We investigate the connections between Ramsey properties of Fraïssé classes $\mathcal {K}$ and the universal minimal flow $M(G_\mathcal {K})$ of the automorphism group $G_\mathcal {K}$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class $\mathcal {K}$ has finite Ramsey degree for embeddings, then this degree equals the size of $M(G_\mathcal {K})$. We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if $\mathcal {K}$ is a relational Ramsey class and $G_\mathcal {K}$ is amenable, then $M(G_\mathcal {K})$ admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.
