On Σ1 1 equivalence relations with Borel classes of bounded rank

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

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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DOI 10.2307/2274278
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Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.

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Π11 Borel Sets.Alexander S. Kechris, David Marker & Ramez L. Sami - 1989 - Journal of Symbolic Logic 54 (3):915 - 920.

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