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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On extending actions


Author: Robert Vaught
Journal: Proc. Amer. Math. Soc. 107 (1989), 1087-1090
MSC: Primary 54H05; Secondary 54H15
DOI: https://doi.org/10.1090/S0002-9939-1989-0962248-2
MathSciNet review: 962248
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Abstract: Consider a Polish topological group $ G$ acting via $ J$ on a substandard (= countably generated) Borel space. Theorem 1. Any such "Borel action" can be extended to a Borel action $ J':G \times X' \to X'$ where $ X'$ is coanalytic. (Theorem 3 gives an analogue for continuous actions.) Corollary 2. The result "in any Borel action, orbits are Borel" implies the (well-known) result "all such orbits are absolutely Borel".


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DOI: https://doi.org/10.1090/S0002-9939-1989-0962248-2
Article copyright: © Copyright 1989 American Mathematical Society