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Mixed systems

C. J. Ash & J. F. Knight

Journal of Symbolic Logic 59 (4):1383-1399 (1994)

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Hyperarithmetical relations in expansions of recursive structures.Alan D. Vlach - 1994 - Annals of Pure and Applied Logic 66 (2):163-196.details Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...) Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark
Coding a family of sets.J. F. Knight - 1998 - Annals of Pure and Applied Logic 94 (1-3):127-142.details In this paper, we state a metatheorem for constructions involving coding. Using the metatheorem, we obtain results on coding a family of sets into a family of relations, or into a single relation. For a concrete example, we show that the set of limit points in a recursive ordering of type ω 2 can have arbitrary 2-REA degree. Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 1 citation
Ramified systems.C. J. Ash & J. F. Knight - 1994 - Annals of Pure and Applied Logic 70 (3):205-221.details Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 8 citations
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 (...) Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 8 citations

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