Equivalence Relations Which Are Borel Somewhere

2015/11/25 by William Chan, Chan, William
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1511.07981

Made some minor changes and corrected some typos. Added some new remarks at the end. Included funding information

arxiv created 2015/12/08 · arxiv updated 2015/12/09

Abstract

The following will be shown: Let I be a σ-ideal on a Polish space X with the property that the associated forcing of I⁺ Borel subsets ordered by ⊆ is a proper forcing. Let E be an analytic or coanalytic equivalence relation on this Polish space with all equivalence classes Borel. If sharps of certain sets exist, then there is an I⁺ Borel subset C of X such that E \upharpoonright C is a Borel equivalence relation.

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