On very high degrees

Journal of Symbolic Logic 73 (1):309-342 (2008)
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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

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Citations of this work

Splitting into degrees with low computational strength.Rod Downey & Keng Meng Ng - 2018 - Annals of Pure and Applied Logic 169 (8):803-834.
Strong Jump-Traceability.Noam Greenberg & Dan Turetsky - 2018 - Bulletin of Symbolic Logic 24 (2):147-164.
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A superhigh diamond in the c.e. tt-degrees.Douglas Cenzer, Johanna Ny Franklin, Jiang Liu & Guohua Wu - 2011 - Archive for Mathematical Logic 50 (1-2):33-44.

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References found in this work

Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
[Omnibus Review].Rod Downey - 1997 - Journal of Symbolic Logic 62 (3):1048-1055.
Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.
Completing pseudojump operators.R. Coles, R. Downey, C. Jockusch & G. LaForte - 2005 - Annals of Pure and Applied Logic 136 (3):297-333.

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