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Original Paper
Quasi-complements of the cappable degrees
Article first published online: 3 FEB 2004
DOI: 10.1002/malq.200310089
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
Wu, G. (2004), Quasi-complements of the cappable degrees. Mathematical Logic Quarterly, 50: 189–201. doi: 10.1002/malq.200310089
Publication History
- Issue published online: 3 FEB 2004
- Article first published online: 3 FEB 2004
- Manuscript Accepted: 23 DEC 2003
- Manuscript Revised: 22 DEC 2003
- Manuscript Received: 22 MAY 2003
- Abstract
- References
- Cited By
Keywords:
- Cappable degree;
- high/low hierarchy;
- quasi-complement
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 low2 quasi-complement. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)