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Quasi-complements of the cappable degrees

✍ Scribed by Guohua Wu

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 208 KB
Volume: 50
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310089

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✦ Synopsis

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 (due to Shore) 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 low~2~ quasi‐complement. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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