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March 2011 Benign cost functions and lowness properties
Noam Greenberg, André Nies
J. Symbolic Logic 76(1): 289-312 (March 2011). DOI: 10.2178/jsl/1294171001

Abstract

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 functions, 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 superlow c.e. degrees and thus gives a use of algorithmic randomness in the study of the c.e. Turing degrees.

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Noam Greenberg. André Nies. "Benign cost functions and lowness properties." J. Symbolic Logic 76 (1) 289 - 312, March 2011. https://doi.org/10.2178/jsl/1294171001

Information

Published: March 2011
First available in Project Euclid: 4 January 2011

zbMATH: 1221.03036
MathSciNet: MR2791349
Digital Object Identifier: 10.2178/jsl/1294171001

Rights: Copyright © 2011 Association for Symbolic Logic

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