Joining to high degrees via noncuppables

Archive for Mathematical Logic 49 (2):195-211 (2010)

Abstract
Cholak, Groszek and Slaman proved in J Symb Log 66:881–901, 2001 that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree by a low2 c.e. degree b. It is natural to ask in which subclass of low2 c.e. degrees can b in Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) be located. Wu proved in Math Log Quart 50:189–201, 2004 that b can be cappable. We prove in this paper that b in Jockusch, Li and Yang’s result can be noncuppable, improving both Jockusch, Li and Yang, and Wu’s results
Keywords High degrees  Noncuppable degrees  Gap-cogap argument
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DOI 10.1007/s00153-009-0165-z
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References found in this work BETA

An Almost Deep Degree.Peter Cholak, Marcia Groszek & Theodore Slaman - 2001 - Journal of Symbolic Logic 66 (2):881-901.
Quasi-Complements of the Cappable Degrees.Guohua Wu - 2004 - Mathematical Logic Quarterly 50 (2):189.

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