Isomorphism and Bi-Embeddability Relations on Computable Structures∗
نویسندگان
چکیده
We study the complexity of natural equivalence relations on classes of computable structures such as isomorphism and bi-embeddability. We use the notion of tc-reducibility to show completeness of the isomorphism relation on many familiar classes in the context of all Σ1 equivalence relations on hyperarithmetical subsets of ω. We also show that the bi-embeddability relation on an appropriate hyperarithmetical class of computable structures may have the same complexity as any given Σ1 equivalence relation on ω. ∗The first and the second authors acknowledge the generous support of the FWF through projects M 1188 N13 and P 19898 N18. Fokina, Harizanov, Knight, and McCoy were partially supported by the NSF binational grant DMS-0554841. Harizanov was partially supported by the NSF grant DMS-0904101.
منابع مشابه
Workshop in Computability Theory Paris - July 2010
A pair of sets of natural numbers A and B forms a K-pair if there exists a c.e. set W , such that A × B ⊆ W and A × B ⊆ W . Kpairs are introduced by Kalimullin and used by him to prove the first order definability of the enumeration jump operator in the global structure of the enumeration degrees. He shows that the property of being a K-pair is degree theoretic and first order definable in the ...
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