Generics in invariant subsets of some highly homogeneous permutation groups

Fuente: arXiv
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Main Authors: Drzewiecka, Monika, Ivanov, Aleksander, Mokry, Bartosz
Format: Preprint
Published: 2023
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author Drzewiecka, Monika
Ivanov, Aleksander
Mokry, Bartosz
author_facet Drzewiecka, Monika
Ivanov, Aleksander
Mokry, Bartosz
contents Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the family of finite partial maps extendable to elements of this conjugacy class has the cofinal amalgamation property. Similar statements are proved for automorphisms of typical ultrahomogeneous partial orderings.
format Preprint
id arxiv_https___arxiv_org_abs_2303_07915
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Generics in invariant subsets of some highly homogeneous permutation groups
Drzewiecka, Monika
Ivanov, Aleksander
Mokry, Bartosz
Logic
Group Theory
03C64, 03E15, 20B27
Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the family of finite partial maps extendable to elements of this conjugacy class has the cofinal amalgamation property. Similar statements are proved for automorphisms of typical ultrahomogeneous partial orderings.
title Generics in invariant subsets of some highly homogeneous permutation groups
topic Logic
Group Theory
03C64, 03E15, 20B27
url https://arxiv.org/abs/2303.07915