Generics in invariant subsets of some highly homogeneous permutation groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908329934061568 |
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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 |