Amenability and Ramsey theory

• Autorzy: Justin Tatch Moore
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20F65: Geometric group theory
• 03E02: Partition relations
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 05D10: Ramsey theory
• 03C15: Denumerable structures
• 20F38: Other groups related to topology or analysis
• 05C55: Generalized Ramsey theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 3
• Strony: 263-280

Daty

wydano

2013

Twórcy

autor

Justin Tatch Moore

• Department of Mathematics, Cornell University, 555 Malott Hall, Ithaca, NY 14853-4201, U.S.A.

Identyfikatory

DOI

10.4064/fm220-3-6