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- W4384268544 abstract "Let $G$ be a closed permutation group on a countably infinite set $Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any p.m.p. ergodic action $Gcurvearrowright (X,mu)$ is either essentially free or essentially transitive. A key notion that we develop in our approach is that of invariant random expansions, which are $G$-invariant probability measures on the space of expansions of the canonical (model theoretic) structure associated with $G$. We also initiate the study of invariant random subgroups for Polish groups and prove that -- although the result for p.m.p. ergodic actions fails for the group $mathrm{Sym}(Omega)$ of all permutation of $Omega$ -- any ergodic invariant random subgroup of $mathrm{Sym}(Omega)$ is essentially transitive." @default.
- W4384268544 created "2023-07-14" @default.
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- W4384268544 creator A5064979338 @default.
- W4384268544 date "2023-07-12" @default.
- W4384268544 modified "2023-10-17" @default.
- W4384268544 title "Stabilizers for ergodic actions and invariant random expansions of non-archimedean Polish groups" @default.
- W4384268544 doi "https://doi.org/10.48550/arxiv.2307.06253" @default.
- W4384268544 hasPublicationYear "2023" @default.
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