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On very high degrees

Published online by Cambridge University Press:  12 March 2014

Keng Meng Ng
Keng Meng Ng*
Affiliation:
School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, PO BOX 600, Wellington, New Zealand, E-mail: Keng.Meng.Ng@mcs.vuw.ac.nz
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Abstract

In this paper we show that there is a pair of superhigh r.e. degree that forms a minimal pair. An analysis of the proof shows that a critical ingredient is the growth rates of certain order functions. This leads us to investigate certain high r.e. degrees, which resemble ∅′ very closely in terms of ∅′-jump traceability. In particular, we will construct an ultrahigh degree which is cappable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 1 , March 2008 , pp. 309 - 342
Copyright
Copyright © Association for Symbolic Logic 2008

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