Topological dynamics of unordered Ramsey structures

Moritz Müller; András Pongrácz

Fundamenta Mathematicae (2015)

  • Volume: 230, Issue: 1, page 77-98
  • ISSN: 0016-2736

Abstract

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We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow M ( G ) of the automorphism group G of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of M ( G ) . We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and G is amenable, then M ( G ) admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.

How to cite

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Moritz Müller, and András Pongrácz. "Topological dynamics of unordered Ramsey structures." Fundamenta Mathematicae 230.1 (2015): 77-98. <http://eudml.org/doc/283027>.

@article{MoritzMüller2015,
abstract = {We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow $M(G_)$ of the automorphism group $G_$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of $M(G_)$. We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and $G_$ is amenable, then $M(G_)$ admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.},
author = {Moritz Müller, András Pongrácz},
journal = {Fundamenta Mathematicae},
keywords = {finite flow; Ramsey; amenable; measure concentration},
language = {eng},
number = {1},
pages = {77-98},
title = {Topological dynamics of unordered Ramsey structures},
url = {http://eudml.org/doc/283027},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Moritz Müller
AU - András Pongrácz
TI - Topological dynamics of unordered Ramsey structures
JO - Fundamenta Mathematicae
PY - 2015
VL - 230
IS - 1
SP - 77
EP - 98
AB - We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow $M(G_)$ of the automorphism group $G_$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of $M(G_)$. We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and $G_$ is amenable, then $M(G_)$ admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.
LA - eng
KW - finite flow; Ramsey; amenable; measure concentration
UR - http://eudml.org/doc/283027
ER -

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