Possible degrees in recursive copies II

Annals of Pure and Applied Logic 87 (2):151-165 (1997)
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Abstract

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 of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA

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References found in this work

Pairs of recursive structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Intrinsically gs;0alpha; relations.E. Barker - 1988 - Annals of Pure and Applied Logic 39 (2):105-130.
Pairs of computable structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Intrinsically< i> gs_;< sup> 0< sub> alpha; relations.E. Barker - 1988 - Annals of Pure and Applied Logic 39 (2):105-130.

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