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  1. Turing degrees of certain isomorphic images of computable relations.Valentina S. Harizanov - 1998 - Annals of Pure and Applied Logic 93 (1-3):103-113.
    A model is computable if its domain is a computable set and its relations and functions are uniformly computable. Let be a computable model and let R be an extra relation on the domain of . That is, R is not named in the language of . We define to be the set of Turing degrees of the images f under all isomorphisms f from to computable models. We investigate conditions on and R which are sufficient and necessary for to (...)
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  • Generalized weak presentations.Alexandra Shlapentokh - 2002 - Journal of Symbolic Logic 67 (2):787-819.
    Let K be a computable field. Let F be a collection of recursive functions over K, possibly including field operations. We investigate the following question. Given an r.e. degree a, is there an injective map j: K $\longrightarrow \mathbb{N}$ such that j(K) is of degree a and all the functions in F are translated by restrictions of total recursive functions.
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  • Turing degrees of hypersimple relations on computable structures.Valentina S. Harizanov - 2003 - Annals of Pure and Applied Logic 121 (2-3):209-226.
    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 (...)
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