Equivalence Relations That Are Σ03 Complete for Computable Reducibility - (Extended Abstract)
نویسندگان
چکیده
Let E,F be equivalence relations on N. We say that E is computably reducible to F , written E ≤ F , if there is a computable function p : N→ N such that xEy ↔ p(x)Fp(y). We show that several natural Σ 3 equivalence relations are in fact Σ 3 complete for this reducibility. Firstly, we show that one-one equivalence of computably enumerable sets, as an equivalence relation on indices, is Σ 3 complete. Thereafter, we show that this equivalence relation is below the computable isomorphism relation on computable structures from classes including predecessor trees, Boolean algebras, and metric spaces. This establishes the Σ 3 completeness of these isomorphism relations.
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