Amenability and Ramsey Theory
Group Theory
2011-10-21 v4 Combinatorics
Functional Analysis
Logic
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 Folner 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.
Cite
@article{arxiv.1106.3127,
title = {Amenability and Ramsey Theory},
author = {Justin Tatch Moore},
journal= {arXiv preprint arXiv:1106.3127},
year = {2011}
}
Comments
18 pages. Section 6 was expanded to contain a generalization of the main results to automorphism groups of Fraisse structures. Several typos fixed throughout, including mathematical typos (missing 1/2's) in the proof of 2.1