Topological dynamics of unordered Ramsey structures

• Autorzy: Moritz Müller , András Pongrácz
• Języki publikacji: EN

Abstrakty

EN

We investigate the connections between Ramsey properties of Fraïssé classes 𝒦 and the universal minimal flow $M(G_𝒦)$ of the automorphism group $G_𝒦$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) 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 (2014) 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.

Kategorie tematyczne

• 03C15: Denumerable structures
• 05C55: Generalized Ramsey theory
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 1
• Strony: 77-98

Daty

wydano

2015

Twórcy

autor

Moritz Müller

• Kurt Gödel Research Center (KGRC), 1090 Wien, Austria

autor

András Pongrácz

• Laboratoire d'Informatique (LIX), École Polytechnique, 91128 Palaiseau, France

Identyfikatory

DOI

10.4064/fm230-1-3