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arXiv · 1401.7766

Topological dynamics of unordered Ramsey structures

Moritz Müller·András Pongrácz
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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.

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Moritz Müller, András Pongrácz. 2014-04-24. Topological dynamics of unordered Ramsey structures. https://arxiv.org/abs/1401.7766

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