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An almost-universal cupping degree

Published online by Cambridge University Press:  12 March 2014

Jiang Liu  and
Guohua Wu
Jiang Liu*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Guohua Wu
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore, E-mail: [email protected]
*
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, P.R. China, E-mail: [email protected]
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Abstract

Say that an incomplete d.r.e. degree has almost universal cupping property, if it cups all the r.e. degrees not below it to 0′. In this paper, we construct such a degree d, with all the r.e. degrees not cupping d to 0′ bounded by some r.e. degree strictly below d. The construction itself is an interesting 0″′ argument and this new structural property can be used to study final segments of various degree structures in the Ershov hierarchy.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1137 - 1152
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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