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- W3037826954 abstract "This paper considers cardinalities arising from Polish group actions. The first part of the paper answers a question of Becker-Kechris by showing that under suitable determinacy assumptions in ZF+DC, every action by a Polish group on a metric space is either as complicated as the Vitali equivalence relation or no more complicated than the equality relation on bounded subsets of aleph_1. The same argument shows that if hereditarily wellorderabel sets can be used as complete invariants, then elements in HC will do. The second half gives a new proof of Howard Becker's recent theorem that Vaught's conjecture holds for groups with a left invariant complete metric. The proof also serves to show that Vaught's conjecture holds for such groups on Sigma^1_1 sets (in ZFC) and reasonably definable sets under large cardinal assumptions." @default.
- W3037826954 created "2020-07-02" @default.
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- W3037826954 date "1996-11-07" @default.
- W3037826954 modified "2023-09-27" @default.
- W3037826954 title "Orbit cardinalities" @default.
- W3037826954 hasPublicationYear "1996" @default.
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