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

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
Categories (categorize this paper)
DOI 10.1002/malq.200310089
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 54,431
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Joining to High Degrees Via Noncuppables.Jiang Liu & Guohua Wu - 2010 - Archive for Mathematical Logic 49 (2):195-211.

Add more citations

Similar books and articles

On a Conjecture of Lempp.Angsheng Li - 2000 - Archive for Mathematical Logic 39 (4):281-309.
Bounding Cappable Degrees.Angsheng Li - 2000 - Archive for Mathematical Logic 39 (5):311-352.
The Computably Enumerable Degrees Are Locally Non-Cappable.Matthew B. Giorgi - 2003 - Archive for Mathematical Logic 43 (1):121-139.
On Very High Degrees.Keng Meng Ng - 2008 - Journal of Symbolic Logic 73 (1):309-342.
Joining to High Degrees Via Noncuppables.Jiang Liu & Guohua Wu - 2010 - Archive for Mathematical Logic 49 (2):195-211.
Complementing Cappable Degrees in the Difference Hierarchy.Rod Downey, Angsheng Li & Guohua Wu - 2004 - Annals of Pure and Applied Logic 125 (1-3):101-118.
Non‐Isolated Quasi‐Degrees.Ilnur I. Batyrshin - 2009 - Mathematical Logic Quarterly 55 (6):587-597.
Complementation in the Turing Degrees.Theodore A. Slaman & John R. Steel - 1989 - Journal of Symbolic Logic 54 (1):160-176.
Badness and Jump Inversion in the Enumeration Degrees.Charles M. Harris - 2012 - Archive for Mathematical Logic 51 (3-4):373-406.
On the Jump Classes of Noncuppable Enumeration Degrees.Charles M. Harris - 2011 - Journal of Symbolic Logic 76 (1):177 - 197.


Added to PP index

Total views
13 ( #702,036 of 2,374,855 )

Recent downloads (6 months)
1 ( #559,821 of 2,374,855 )

How can I increase my downloads?


My notes