  We prove that if every real belongs to a set generic extension of the
constructible universe then every \Sigma_1^1 equivalence E on reals either
admits a Delta_1^HC reduction to the equality on the set 2^{<\om_1} of all
countable binary sequences, or continuously embeds E_0, the Vitali equivalence.
  The proofs are based on a topology generated by OD sets.
