Incomparability in local structures of s -degrees and Q -degrees

Archive for Mathematical Logic 59 (7-8):777-791 (2020)
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Abstract

We show that for every intermediate \ s-degree there exists an incomparable \ s-degree. As a consequence, for every intermediate \ Q-degree there exists an incomparable \ Q-degree. We also show how these results can be applied to provide proofs or new proofs of upper density results in local structures of s-degrees and Q-degrees.

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Mathematical Logic Quarterly 5 (7‐13):117-125.
On minimal pairs of enumeration degrees.Kevin McEvoy & S. Barry Cooper - 1985 - Journal of Symbolic Logic 50 (4):983-1001.

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