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Published September 2017 | Submitted
Journal Article Open

Equivalence Relations Which Are Borel Somewhere

Chan, William


The following will be shown: Let I be a σ-ideal on a Polish space X so that the associated forcing of I + Δ^1_1 sets ordered by ⊆ is a proper forcing. Let E be a Σ^1_1 or a ∏^1_1 equivalence relation on X with all equivalence classes Δ^1_1. If for all z ∈_H(2^N0)+, z ♯ exists, then there exists an I + Δ^1_1 set C ⊆ X such that E ↾ C is a Δ^1_1 equivalence relation.

Additional Information

© 2017 The Association for Symbolic Logic. Published online: 08 September 2017. Research partially supported by NSF grants DMS-1464475 and EMSW21-RTG DMS-1044448.

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August 19, 2023
October 17, 2023