Maximal contiguous degrees

Journal of Symbolic Logic 67 (1):409-437 (2002)
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Abstract

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas

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Citations of this work

A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.

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References found in this work

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
Wtt-degrees and t-degrees of R.e. Sets.Michael Stob - 1983 - Journal of Symbolic Logic 48 (4):921-930.

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