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2008 Undecidability of local structures of $\mathrm{s}$-degrees and $\mathrm{Q}$-degrees
Maria Libera Affatato, Thomas F. Kent, Andrea Sorbi
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Tbilisi Math. J. 1: 15-32 (2008). DOI: 10.32513/tbilisi/1528768822

Abstract

We show that the first order theory of the $\Sigma^0_2\;$ $\mathrm{s}$-degrees is undecidable. Via isomorphism of the $\mathrm{s}$-degrees with the $\mathrm{Q}$-degrees, this also shows that the first order theory of the $\Pi^0_2\;$ $\mathrm{Q}$-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the $\Sigma^0_2\;$ $\mathrm{s}$-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies) that the first order theory of the c.e. $\mathrm{Q}$-degrees is undecidable.

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Maria Libera Affatato. Thomas F. Kent. Andrea Sorbi. "Undecidability of local structures of $\mathrm{s}$-degrees and $\mathrm{Q}$-degrees." Tbilisi Math. J. 1 15 - 32, 2008. https://doi.org/10.32513/tbilisi/1528768822

Information

Received: 5 September 2007; Revised: 9 November 2007; Accepted: 11 December 2007; Published: 2008
First available in Project Euclid: 12 June 2018

zbMATH: 1158.03028
MathSciNet: MR2434435
Digital Object Identifier: 10.32513/tbilisi/1528768822

Subjects:
Primary: 03D35
Secondary: 03D25, 03D30

Rights: Copyright © 2008 Tbilisi Centre for Mathematical Sciences

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