Maximal contiguous degrees

Journal of Symbolic Logic 67 (1):409-437 (2002)
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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DOI 10.2178/jsl/1190150052
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References found in this work BETA
Splitting Theorems in Recursion Theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
Highness and Bounding Minimal Pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.
Structural Interactions of the Recursively Enumerable T- and W-Degrees.R. G. Downey & M. Stob - 1986 - Annals of Pure and Applied Logic 31 (2):205-236.

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

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