## 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.## References

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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- 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