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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1303127
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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 $ {\mathbf{Z}}$-actions to actions by arbitrary countable groups. We show that the $ \sigma $-ideal of closed smooth sets is $ \Pi _1^1$ non-Borel.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1303127-8
PII: S 0002-9947(1995)1303127-8
Keywords: Borel equivalence relations, negligible sets, $ \sigma $-ideals of compact sets, group actions, wandering sets
Article copyright: © Copyright 1995 American Mathematical Society