Ordered structures and large conjugacy classes
| Autor: | Maciej Malicki, Aleksandra Kwiatkowska |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Algebra and Number Theory Group (mathematics) 010102 general mathematics Diagonal Automorphism 01 natural sciences Combinatorics Mathematics::Group Theory Mathematics::Logic Conjugacy class Limit (category theory) 0103 physical sciences 010307 mathematical physics Tree (set theory) 0101 mathematics Partially ordered set Mathematics |
| Zdroj: | Journal of Algebra. 557:67-96 |
| ISSN: | 0021-8693 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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