Ordered structures and large conjugacy classes

JOURNAL OF ALGEBRA

卷:557

Article

Kwiatkowska, Aleksandra^1,2  Malicki, Maciej³ 

[1] Uniwersytet Wroclawski, Inst Matematy, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[2] Univ Munster, Inst Math Log & Grundlagenforsch, Einsteinstr 62, D-48149 Munster, Germany

[3] Warsaw Sch Econ, Dept Math & Math Econ, Niepodleglosci 162, PL-02554 Warsaw, Poland

关键词: Polish non-archimedean groups;    Ample generics;    Extreme amenability;   

DOI  :  10.1016/j.jalgebra.2020.03.021

来源: Elsevier

【 摘 要 】

This article is a contribution to the following problem: does there exist a Polish non-archimedean group (equivalently: automorphism group of a Fraisse limit) that is extremely amenable, and has ample generics. As Fraisse limits whose automorphism groups are extremely amenable must be ordered, i.e., equipped with a linear ordering, we focus on ordered Fraisse limits. We prove that automorphism groups of the universal ordered boron tree, and the universal ordered poset have a comeager conjugacy class but no comeager 2-dimensional diagonal conjugacy class. We formulate general conditions implying that there is no comeager conjugacy class, comeager 2-dimensional diagonal conjugacy class or non-meager 2-dimensional topological similarity class in the automorphism group of an ordered Fraisse limit. We also provide a number of applications of these results. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free