Quasi-complements of the cappable degrees

Mathematical Logic Quarterly 50 (2):189 (2004)
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Abstract

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

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10.1002/malq.200310089

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Citations of this work

Joining to high degrees via noncuppables.Jiang Liu & Guohua Wu - 2010 - Archive for Mathematical Logic 49 (2):195-211.

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References found in this work

The upper semilattice of degrees ≤ 0' is complemented.David B. Posner - 1981 - Journal of Symbolic Logic 46 (4):705 - 713.
An almost deep degree.Peter Cholak, Marcia Groszek & Theodore Slaman - 2001 - Journal of Symbolic Logic 66 (2):881-901.
Complementation in the Turing degrees.Theodore A. Slaman & John R. Steel - 1989 - Journal of Symbolic Logic 54 (1):160-176.
A cornucopia of minimal degrees.Leonard P. Sasso - 1970 - Journal of Symbolic Logic 35 (3):383-388.
Splitting theorems and the jump operator.R. G. Downey & Richard A. Shore - 1998 - Annals of Pure and Applied Logic 94 (1-3):45-52.

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