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2011 Characterizing the Join-Irreducible Medvedev Degrees
Paul Shafer
Notre Dame J. Formal Logic 52(1): 21-38 (2011). DOI: 10.1215/00294527-2010-034

Abstract

We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi. We use this characterization to prove that there are Medvedev degrees above the second-least degree that do not bound any join-irreducible degrees above this second-least degree. This solves a problem posed by Sorbi and Terwijn. Finally, we prove that the filter generated by the degrees of closed sets is not prime. This solves a problem posed by Bianchini and Sorbi.

Citation

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Paul Shafer. "Characterizing the Join-Irreducible Medvedev Degrees." Notre Dame J. Formal Logic 52 (1) 21 - 38, 2011. https://doi.org/10.1215/00294527-2010-034

Information

Published: 2011
First available in Project Euclid: 13 December 2010

zbMATH: 1232.03029
MathSciNet: MR2747160
Digital Object Identifier: 10.1215/00294527-2010-034

Subjects:
Primary: 03B55, 03D30, 03G10

Rights: Copyright © 2011 University of Notre Dame

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Vol.52 • No. 1 • 2011
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