192 research outputs found
On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes
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
When a partial Borel order is linearizable
We prove the following classification theorem of the ``Glimm -- Effros'' type
for Borel order relations: a Borel partial order on the reals either is Borel
linearizable or includes a copy of a certain Borel partial order \meo which
is not Borel linearizable
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