This is an announcement for the paper "Amenability and Ramsey Theory" by Justin Tatch Moore.

Abstract: 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 F\o lner criterion. As a bi-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.

Archive classification: math.GR math.CO math.FA math.LO

Mathematics Subject Classification: 05D10, 05C55, 20F38, 20F65, 43A07

Remarks: 13 pages. Comments welcome

Submitted from: justin@math.cornell.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.3127

or

http://arXiv.org/abs/1106.3127