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

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
Keywords quasi‐complement  high/low hierarchy  Cappable degree
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DOI 10.1002/malq.200310089
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