Amenability and Ramsey theory

Justin Tatch Moore

Fundamenta Mathematicae (2013)

  • Volume: 220, Issue: 3, page 263-280
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Justin Tatch Moore. "Amenability and Ramsey theory." Fundamenta Mathematicae 220.3 (2013): 263-280. <http://eudml.org/doc/283202>.

@article{JustinTatchMoore2013,
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 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.},
author = {Justin Tatch Moore},
journal = {Fundamenta Mathematicae},
keywords = {amenable; extremely amenable; Fraïssé; Følner criterion; free group; invariant measurability; structural Ramsey theory; Thompson's group; ultrahomogeneous},
language = {eng},
number = {3},
pages = {263-280},
title = {Amenability and Ramsey theory},
url = {http://eudml.org/doc/283202},
volume = {220},
year = {2013},
}

TY - JOUR
AU - Justin Tatch Moore
TI - Amenability and Ramsey theory
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 3
SP - 263
EP - 280
AB - 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.
LA - eng
KW - amenable; extremely amenable; Fraïssé; Følner criterion; free group; invariant measurability; structural Ramsey theory; Thompson's group; ultrahomogeneous
UR - http://eudml.org/doc/283202
ER -

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