On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model
Logic
2018-08-22 v1
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.
Cite
@article{arxiv.math/9507213,
title = {On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model},
author = {Vladimir Kanovei},
journal= {arXiv preprint arXiv:math/9507213},
year = {2018}
}