On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes
Vladimir Kanovei
Abstract
We prove that if every real belongs to a set generic extension of the constructible universe then every Σ11 equivalence E on reals either admits a Delta1HC reduction to the equality on the set 2<1 of all countable binary sequences, or continuously embeds E0, the Vitali equivalence. The proofs are based on a topology generated by OD sets.
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