Notre Dame Journal of Formal Logic

Characterizing the Join-Irreducible Medvedev Degrees

Paul Shafer


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.

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Notre Dame J. Formal Logic, Volume 52, Number 1 (2011), 21-38.

First available in Project Euclid: 13 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03D30: Other degrees and reducibilities 03G10: Lattices and related structures [See also 06Bxx] 03B55: Intermediate logics

Medvedev degrees lattices Brouwer algebras intermediate logics


Shafer, Paul. Characterizing the Join-Irreducible Medvedev Degrees. Notre Dame J. Formal Logic 52 (2011), no. 1, 21--38. doi:10.1215/00294527-2010-034.

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