Topological dynamics of unordered Ramsey structures
Logic
2014-04-25 v2
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.
Keywords
Cite
@article{arxiv.1401.7766,
title = {Topological dynamics of unordered Ramsey structures},
author = {Moritz Müller and András Pongrácz},
journal= {arXiv preprint arXiv:1401.7766},
year = {2014}
}