Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures

Notre Dame Journal of Formal Logic 43 (1):51-64 (2002)
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Abstract

We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or

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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.
Pairs of Computable Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Turing Degrees of Certain Isomorphic Images of Computable Relations.Valentina S. Harizanov - 1998 - Annals of Pure and Applied Logic 93 (1-3):103-113.

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