Equivalence Relations Which Are Borel Somewhere

William Chan

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arXiv · 1511.07981

Equivalence Relations Which Are Borel Somewhere

William Chan

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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 $\subseteq$ 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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William Chan. 2015-12-08. Equivalence Relations Which Are Borel Somewhere. https://arxiv.org/abs/1511.07981

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