Geodesic
Amenability and Ramsey theory
Justin Tatch Moore1
1 Department of Mathematics Cornell University 555 Malott Hall Ithaca, NY 14853-4201, U.S.A.
Fundamenta Mathematicae, Tome 220 (2013) no. 3, pp. 263-280

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group $G$, there is a subset $E$ of $G$ such that no finitely additive probability measure on $G$ measures all translates of $E$ equally. The analysis of discrete groups will be generalized to the setting of automorphism groups of ultrahomogeneous structures.
DOI : 10.4064/fm220-3-6
Keywords: purpose article connect notion amenability discrete group form structural ramsey theory ramsey theoretic reformulation amenability constitutes considerable weakening lner criterion by product shown non amenable group there subset finitely additive probability measure measures translates equally analysis discrete groups generalized setting automorphism groups ultrahomogeneous structures

Justin Tatch Moore 1

1 Department of Mathematics Cornell University 555 Malott Hall Ithaca, NY 14853-4201, U.S.A. 
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Justin Tatch Moore. Amenability and Ramsey theory. Fundamenta Mathematicae, Tome 220 (2013) no. 3, pp. 263-280. doi: 10.4064/fm220-3-6

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