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On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model

Vladimir Kanovei
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Abstract

We prove that in Solovay model every OD equivalence E on reals either admits an OD reduction to the equality on the set of all countable (of length < omega_1) binary sequences, or continuously embeds E_0, the Vitali equivalence. If E is a Sigma_1^1 (resp. Sigma_1^2) relation then the reduction in the ``either'' part can be chosen in the class of all Delta_1 (resp. Delta_2) functions. The proofs are based on a topology generated by OD sets.

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Vladimir Kanovei. 1995-07-26. On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model. https://doi.org/10.2307/2275646

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