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March 2002 Maximal contiguous degrees
Peter Cholak, Rod Downey, Stephen Walk
J. Symbolic Logic 67(1): 409-437 (March 2002). DOI: 10.2178/jsl/1190150052

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

Citation

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Peter Cholak. Rod Downey. Stephen Walk. "Maximal contiguous degrees." J. Symbolic Logic 67 (1) 409 - 437, March 2002. https://doi.org/10.2178/jsl/1190150052

Information

Published: March 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1007.03041
MathSciNet: MR1889559
Digital Object Identifier: 10.2178/jsl/1190150052

Subjects:
Primary: 03D25

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.67 • No. 1 • March 2002
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