The partial orderings of the computably enumerable ibT-degrees and cl-degrees are not elementarily equivalent

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Annals of Pure and Applied Logic 164 (5):577-588 (2013)
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Abstract

We show that, in the partial ordering of the computably enumerable computable Lipschitz degrees, there is a degree a>0a>0 such that the class of the degrees which do not cup to a is not bounded by any degree less than a. Since Ambos-Spies [1] has shown that, in the partial ordering of the c.e. identity-bounded Turing degrees, for any degree a>0a>0 the degrees which do not cup to a are bounded by the 1-shift a+1a+1 of a where a+1

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10.1016/j.apal.2012.11.002

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Classical recursion theory: the theory of functions and sets of natural numbers.Piergiorgio Odifreddi - 1989 - New York, N.Y., USA: Sole distributors for the USA and Canada, Elsevier Science Pub. Co..
Computability theory and differential geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.
The computable Lipschitz degrees of computably enumerable sets are not dense.Adam R. Day - 2010 - Annals of Pure and Applied Logic 161 (12):1588-1602.

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