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Recursive properties of relations on models

Geoffrey R. Hird

Annals of Pure and Applied Logic 63 (3):241-269 (1993)

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Recursive properties of relations on models.Geoffrey R. Hird - 1993 - Annals of Pure and Applied Logic 63 (3):241-269.details Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to S remains r.e., (...) Download Export citation Bookmark 6 citations
Inseparability in recursive copies.Kevin J. Davey - 1994 - Annals of Pure and Applied Logic 68 (1):1-52.details In [7] and [8], it is established that given any abstract countable structure S and a relation R on S, then as long as S has a recursive copy satisfying extra decidability conditions, R will be ∑0α on every recursive copy of S iff R is definable in S by a special type of infinitary formula, a ∑rα() formula. We generalize the typ e of constructions of these papers to produce conditions under which, given two disjoint relations R1 and R2 (...) Download Export citation Bookmark
Possible degrees in recursive copies II.C. J. Ash & J. F. Knight - 1997 - Annals of Pure and Applied Logic 87 (2):151-165.details We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...) Download Export citation Bookmark 8 citations
Quasi-simple relations in copies of a given recursive structure.C. J. Ash, J. F. Knight & J. B. Remmel - 1997 - Annals of Pure and Applied Logic 86 (3):203-218.details Download Export citation Bookmark 4 citations
Turing degrees of hypersimple relations on computable structures.Valentina S. Harizanov - 2003 - Annals of Pure and Applied Logic 121 (2-3):209-226.details Let be an infinite computable structure, and let R be an additional computable relation on its domain A. The syntactic notion of formal hypersimplicity of R on , first introduced and studied by Hird, is analogous to the computability-theoretic notion of hypersimplicity of R on A, given the definability of certain effective sequences of relations on A. Assuming that R is formally hypersimple on , we give general sufficient conditions for the existence of a computable isomorphic copy of on whose (...) Download Export citation Bookmark

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