Generics in invariant subsets of some highly homogeneous permutation groups

Monika Drzewiecka; Aleksander Ivanov; Bartosz Mokry

doi:10.1016/j.apal.2025.103585

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arXiv · 2303.07915

Generics in invariant subsets of some highly homogeneous permutation groups

Monika Drzewiecka·Aleksander Ivanov·Bartosz Mokry

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Abstract

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.

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Monika Drzewiecka, Aleksander Ivanov, Bartosz Mokry. 2023-03-14. Generics in invariant subsets of some highly homogeneous permutation groups. https://doi.org/10.1016/j.apal.2025.103585

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