On Σ1 1 equivalence relations with Borel classes of bounded rank

Journal of Symbolic Logic 49 (4):1273 - 1283 (1984)
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Abstract

In Baire space N = ω ω we define a sequence of equivalence relations $\langle E_\nu| \nu , each E v being Σ 1 1 with classes in Π 0 1 + ν + 1 and such that (i) E ν does not have perfectly many classes, and (ii) N/E ν is countable iff $\omega^L_\nu . This construction can be extended cofinally in (δ 1 3 ) L . A new proof is given of a theorem of Hausdorff on partitions of R into ω 1 many Π 0 3 sets

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Citations of this work

Π11 Borel sets.Alexander S. Kechris, David Marker & Ramez L. Sami - 1989 - Journal of Symbolic Logic 54 (3):915 - 920.
On effective σ‐boundedness and σ‐compactness.Vladimir Kanovei & Vassily Lyubetsky - 2013 - Mathematical Logic Quarterly 59 (3):147-166.

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References found in this work

Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
Higher set theory and mathematical practice.Harvey M. Friedman - 1971 - Annals of Mathematical Logic 2 (3):325.

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