Amenability and Ramsey theory
Tom 220 / 2013
Fundamenta Mathematicae 220 (2013), 263-280
MSC: Primary 05D10, 05C55, 20F38, 20F65, 43A07; Secondary 03C15, 03E02.
DOI: 10.4064/fm220-3-6
Streszczenie
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.
