Completely mitotic c.e. degrees and non-jump inversion

Annals of Pure and Applied Logic 132 (2-3):181-207 (2005)
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Abstract

A completely mitotic computably enumerable degree is a c.e. degree in which every c.e. set is mitotic, or equivalently in which every c.e. set is autoreducible. There are known to be low, low2, and high completely mitotic degrees, though the degrees containing non-mitotic sets are dense in the c.e. degrees. We show that there exists an upper cone of c.e. degrees each of which contains a non-mitotic set, and that the completely mitotic c.e. degrees are nowhere dense in the c.e. degrees. We also show that there is a set computably enumerable in and above 0′ which is not the jump of any completely mitotic degree

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References found in this work

Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
A non-inversion theorem for the jump operator.Richard A. Shore - 1988 - Annals of Pure and Applied Logic 40 (3):277-303.
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