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  1. Ulm Classification of Analytic Equivalence Relations in Generic Universes.Vladimir Kanovei - 1998 - Mathematical Logic Quarterly 44 (3):287-303.
  • Analytic Equivalence Relations and Ulm-Type Classifications.Greg Hjorth & Alexander S. Kechris - 1995 - Journal of Symbolic Logic 60 (4):1273-1300.
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  • Two Results on Borel Orders.Alain Louveau - 1989 - Journal of Symbolic Logic 54 (3):865-874.
    We prove two results about the embeddability relation between Borel linear orders: For $\eta$ a countable ordinal, let $2^\eta$ (resp. $2^{<\eta}$) be the set of sequences of zeros and ones of length $\eta$ (resp. $<\eta$), equipped with the lexicographic ordering. Given a Borel linear order $X$ and a countable ordinal $\xi$, we prove the following two facts. (a) Either $X$ can be embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi + 1}$ continuously embeds in $X$. (b) Either $X$ can (...)
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  • Thin Equivalence Relations and Effective Decompositions.Greg Hjorth - 1993 - Journal of Symbolic Logic 58 (4):1153-1164.
    Let E be a Σ1 1 equivalence relation for which there does not exist a perfect set of inequivalent reals. If 0# exists or if V is a forcing extension of L, then there is a good ▵1 2 well-ordering of the equivalence classes.
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  • An Ulm-Type Classification Theorem for Equivalence Relations in Solovay Model.Vladimir Kanovei - 1997 - Journal of Symbolic Logic 62 (4):1333-1351.
    We prove that in the Solovay model, every OD equivalence relation, E, over the reals, either admits an OD reduction to the equality relation on the set of all countable (of length $ ) binary sequences, or continuously embeds E 0 , the Vitali equivalence. If E is a Σ 1 1 (resp. Σ 1 2 ) relation then the reduction above can be chosen in the class of all ▵ 1 (resp. ▵ 2 ) functions. The proofs are based (...)
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  • A Model of Set-Theory in Which Every Set of Reals is Lebesgue Measurable.[author unknown] - 1973 - Journal of Symbolic Logic 38 (3):529-529.
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