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JSYML
2011

Benign cost functions and lowness properties

13 years 6 months ago
Benign cost functions and lowness properties
We show that the class of strongly jump-traceable c.e. sets can be characterised as those which have sufficiently slow enumerations so they obey a class of well-behaved cost function, called benign. This characterisation implies the containment of the class of strongly jump-traceable c.e. Turing degrees in a number of lowness classes, in particular the classes of the degrees which lie below incomplete random degrees, indeed all LR-hard random degrees, and all ω-c.e. random degrees. The last result implies recent results of Diamondstone’s and Ng’s regarding cupping with supwerlow c.e. degrees and thus gives a use of algorithmic randomness in the study of the c.e. Turing degrees.
Noam Greenberg, André Nies
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JSYML
Authors Noam Greenberg, André Nies
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