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Nonhemimaximal degrees and the high/low hierarchy

Published online by Cambridge University Press:  12 March 2014

Fang Chengling  and
Wu Guohua
Fang Chengling
Affiliation:
Division of Mathematical Sciences, School of Physical andMathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore, E-mail: FANG0032@ntu.edu.sgE-mail:, guohua@ntu.edu.sg
Wu Guohua
Affiliation:
Division of Mathematical Sciences, School of Physical andMathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore, E-mail: FANG0032@ntu.edu.sgE-mail:, guohua@ntu.edu.sg
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Abstract

After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low2, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low2 but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0‴ argument. In this paper, we give another construction of such degrees, which is a standard 0″-argument, much simpler than Downey and Stob's construction mentioned above.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 433 - 446
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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