Amenability and Ramsey theory in the metric setting

被引：1

作者：

Kaichouh, Adriane ^{[1
]}

机构：

[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

FUNDAMENTA MATHEMATICAE | 2015年 / 231卷 / 01期

关键词：

amenability; Ramsey theory; continuous logic; model theory for metric structures; Kechris-Pestov-Todorcevic correspondence; automorphism groups;

D O I：

10.4064/fm231-1-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraisse structures, which encompass all Polish groups. As an application, we prove that amenability is a G(delta) condition.

引用

页码：19 / 38

页数：20

共 50 条

[1] Extreme amenability of L0, a Ramsey theorem, and Levy groups
Farah, Ilijas
Solecki, Slawomir
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (02) : 471 - 493
[2] Ramsey classes of topological and metric spaces
Nesetril, Jaroslav
ANNALS OF PURE AND APPLIED LOGIC, 2006, 143 (1-3) : 147 - 154
[3] Ramsey theory and thermodynamics
Shvalb, Nir
Frenkel, Mark
Shoval, Shraga
Bormashenko, Edward
HELIYON, 2023, 9 (02)
[4] The Ramsey theory of Henson graphs
Dobrinen, Natasha
JOURNAL OF MATHEMATICAL LOGIC, 2023, 23 (01)
[5] Ramsey-Turan theory
Simonovits, M
Sós, VT
DISCRETE MATHEMATICS, 2001, 229 (1-3) : 293 - 340
[6] Schreier sets in Ramsey theory
Farmaki, V.
Negrepontis, S.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (02) : 849 - 880
[7] An Excursion into Nonlinear Ramsey Theory
Doss, Adam
Saracino, Dan
Vestal, Donald L., Jr.
GRAPHS AND COMBINATORICS, 2013, 29 (03) : 407 - 415
[8] An Excursion into Nonlinear Ramsey Theory
Adam Doss
Dan Saracino
Donald L. Vestal
Graphs and Combinatorics, 2013, 29 : 407 - 415
[9] RAMSEY THEORY IN NONCOMMUTATIVE SEMIGROUPS
BERGELSON, V
HINDMAN, N
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 330 (01) : 433 - 446
[10] Ramsey theory on Steiner triples
Granath, Elliot
Gyarfas, Andras
Hardee, Jerry
Watson, Trent
Wu, Xiaoze
JOURNAL OF COMBINATORIAL DESIGNS, 2018, 26 (01) : 5 - 11

← 1 2 3 4 5 →