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Cappable recursively enumerable degrees and Post's program

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Abstract

We give a simple structural property which characterizes the r.e. sets whose (Turing) degrees are cappable. Since cappable degrees are incomplete, this may be viewed as a solution of Post's program, which asks for a simple structural property of nonrecursive r.e. sets which ensures incompleteness.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 294, W-6900, Heidelberg, Germany

    Klaus Ambos-Spies & André Nies

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  1. Klaus Ambos-Spies
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  2. André Nies
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Part of this research was done while the authors visited the Mathematical Sciences research Institute, Berkeley

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Ambos-Spies, K., Nies, A. Cappable recursively enumerable degrees and Post's program. Arch Math Logic 32, 51–56 (1992). https://doi.org/10.1007/BF01270394

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  • DOI: https://doi.org/10.1007/BF01270394

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