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The upper semilattice of degrees ≤ 0' is complemented

David B. Posner

Journal of Symbolic Logic 46 (4):705 - 713 (1981)

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Quasi-complements of the cappable degrees.Guohua Wu - 2004 - Mathematical Logic Quarterly 50 (2):189.details Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement. Download Export citation Bookmark 1 citation
The minimal complementation property above 0′.Andrew E. M. Lewis - 2005 - Mathematical Logic Quarterly 51 (5):470-492.details Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). Download Export citation Bookmark
Generic degrees are complemented.Masahiro Kumabe - 1993 - Annals of Pure and Applied Logic 59 (3):257-272.details Download Export citation Bookmark 3 citations
ASH, CJ, Categoricity in hyperarithmetical degrees (1) BALDWIN, JT and HARRINGTON, L., Trivial pursuit: Re-marks on the main gap (3) COOPER, SB and EPSTEIN, RL, Complementing below re-cursively enumerable degrees (1). [REVIEW]Rl Epstein - 1987 - Annals of Pure and Applied Logic 34 (1):311.details Download Export citation Bookmark
Complementing cappable degrees in the difference hierarchy.Rod Downey, Angsheng Li & Guohua Wu - 2004 - Annals of Pure and Applied Logic 125 (1-3):101-118.details We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees. Download Export citation Bookmark
Complementing below recursively enumerable degrees.S. Barry Cooper & Richard L. Epstein - 1987 - Annals of Pure and Applied Logic 34 (1):15-32.details Download Export citation Bookmark 3 citations
(1 other version)Cupping and noncupping in the enumeration degrees of ∑20 sets.S. Barry Cooper, Andrea Sorbi & Xiaoding Yi - 1996 - Annals of Pure and Applied Logic 82 (3):317-342.details We prove the following three theorems on the enumeration degrees of ∑20 sets. Theorem A: There exists a nonzero noncuppable ∑20 enumeration degree. Theorem B: Every nonzero Δ20enumeration degree is cuppable to 0′e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Δ20 enumeration degree with the anticupping property. Download Export citation Bookmark 13 citations
(1 other version)Cupping and noncupping in the enumeration degrees of∑< sub> 2< sup> 0 sets.S. Barry Cooper, Andrea Sorbi & Xiaoding Yi - 1996 - Annals of Pure and Applied Logic 82 (3):317-342.details Download Export citation Bookmark 3 citations

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