Smooth sets for a Borel equivalence relation

Author:
Carlos E. Uzcátegui A.

Journal:
Trans. Amer. Math. Soc. **347** (1995), 2025-2039

MSC:
Primary 03E15; Secondary 04A15, 28A05, 28D99, 54H05, 54H20

DOI:
https://doi.org/10.1090/S0002-9947-1995-1303127-8

MathSciNet review:
1303127

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Abstract | References | Similar Articles | Additional Information

Abstract: We study some properties of smooth Borel sets with respect to a Borel equivalence relation, showing some analogies with the collection of countable sets from a descriptive set theoretic point of view. We found what can be seen as an analog of the hyperarithmetic points in the context of smooth sets. We generalize a theorem of Weiss from -actions to actions by arbitrary countable groups. We show that the -ideal of closed smooth sets is non-Borel.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1303127-8

Keywords:
Borel equivalence relations,
negligible sets,
-ideals of compact sets,
group actions,
wandering sets

Article copyright:
© Copyright 1995
American Mathematical Society