Analytic equivalence relations and Ulm-type classifications

Analytic Equivalence Relations and Ulm-Type Classifications

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. Association for Symbolic Logic is collaborating with JSTO...

Complete Analytic Equivalence Relations

We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e. maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.

Analytic equivalence relations and bi-embeddability

Analytic Equivalence Relations Satisfying Hyperarithmetic-is-recursive

We prove, in ZF+Σ2-determinacy, that for any analytic equivalence relation E, the following three statements are equivalent: (1) E does not have perfectly many classes, (2) E satisfies hyperarithmetic-is-recursive on a cone, and (3) relative to some oracle, for every equivalence class [Y ]E we have that a real X computes a member of the equivalence class if and only if ω 1 ≥ ω [Y ] 1 . We also ...

Definable Transversals of Analytic Equivalence Relations

We examine the circumstances under which certain analytic equivalence relations on Polish spaces have definable transversals.