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Topological dynamics of unordered Ramsey structures

Volume 230 / 2015

Moritz Müller, András Pongrácz 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.

Authors

  • Moritz MüllerKurt Gödel Research Center (KGRC)
    1090 Wien, Austria
    e-mail
  • András PongráczLaboratoire d'Informatique (LIX)
    École Polytechnique
    91128 Palaiseau, France
    e-mail

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