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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-6,
author = {Justin Tatch Moore},
title = {Amenability and Ramsey theory},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {263-280},
zbl = {1263.05114},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-6}
}
Justin Tatch Moore. Amenability and Ramsey theory. Fundamenta Mathematicae, Tome 220 (2013) pp. 263-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-6/