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2002 Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures
Denis R. Hirschfeldt, Walker M. White
Notre Dame J. Formal Logic 43(1): 51-64 (2002). DOI: 10.1305/ndjfl/1071505769

Abstract

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

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Denis R. Hirschfeldt. Walker M. White. "Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures." Notre Dame J. Formal Logic 43 (1) 51 - 64, 2002. https://doi.org/10.1305/ndjfl/1071505769

Information

Published: 2002
First available in Project Euclid: 15 December 2003

zbMATH: 1048.03035
MathSciNet: MR2033315
Digital Object Identifier: 10.1305/ndjfl/1071505769

Subjects:
Primary: 03D45
Secondary: 03C15, 03C57, 03D30, 03D55

Rights: Copyright © 2002 University of Notre Dame

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Vol.43 • No. 1 • 2002
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