Article ID Journal Published Year Pages File Type
10118900 Annals of Pure and Applied Logic 2005 27 Pages PDF
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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Related Topics
Physical Sciences and Engineering Mathematics Logic
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