Cuppability of Simple and Hypersimple Sets

Notre Dame Journal of Formal Logic 48 (3):349-369 (2007)

Abstract

An incomplete degree is cuppable if it can be joined by an incomplete degree to a complete degree. For sets fulfilling some type of simplicity property one can now ask whether these sets are cuppable with respect to a certain type of reducibilities. Several such results are known. In this paper we settle all the remaining cases for the standard notions of simplicity and all the main strong reducibilities

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References found in this work

Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Degrees Joining to 0'. [REVIEW]David B. Posner & Robert W. Robinson - 1981 - Journal of Symbolic Logic 46 (4):714 - 722.
Simplicity of Recursively Enumerable Sets.Robert W. Robinson - 1967 - Journal of Symbolic Logic 32 (2):162-172.
Bounded Immunity and Btt‐Reductions.Stephen Fenner & Marcus Schaefer - 1999 - Mathematical Logic Quarterly 45 (1):3-21.

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