Topological dynamics of unordered Ramsey structures

Moritz Müller; András Pongrácz

Fundamenta Mathematicae, Tome 228 (2015), p. 77-98 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2015-01-01

Zbl 1318.05041

EUDML-ID : urn:eudml:doc:283027

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-3,
     author = {Moritz M\"uller and Andr\'as Pongr\'acz},
     title = {Topological dynamics of unordered Ramsey structures},
     journal = {Fundamenta Mathematicae},
     volume = {228},
     year = {2015},
     pages = {77-98},
     zbl = {1318.05041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-3}
}

Moritz Müller; András Pongrácz. Topological dynamics of unordered Ramsey structures. Fundamenta Mathematicae, Tome 228 (2015) pp. 77-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-3/