Smooth sets for a Borel equivalence relation

Uzcátegui A., Carlos E.

doi:10.1090/S0002-9947-1995-1303127-8

Smooth sets for a Borel equivalence relation
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by Carlos E. Uzcátegui A.

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

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

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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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