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An Ulm-type classification theorem for equivalence relations in Solovay model

Published online by Cambridge University Press:  12 March 2014

Vladimir Kanovei
Vladimir Kanovei*
Affiliation:
Moscow Transport Engineering Institute, E-mail: kanovei@math.uni-wuppertal.de, kanovei@mech.math.msu.su.
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Abstract

We prove that in the Solovay model, every OD equivalence relation, Ε, over the reals, either admits an OD reduction to the equality relation on the set of all countable (of length < ω1) binary sequences, or continuously embeds Ε0, the Vitali equivalence.

If Ε is a (resp. ) relation then the reduction above can be chosen in the class of all Δ1 (resp. Δ2) functions.

The proofs are based on a topology generated by OD sets.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1333 - 1351
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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