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  1. Embeddings of N5 and the Contiguous Degrees.Klaus Ambos-Spies & Peter A. Fejer - 2001 - Annals of Pure and Applied Logic 112 (2-3):151-188.
    Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...)
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  • Completing Pseudojump Operators.R. Coles, R. Downey, C. Jockusch & G. LaForte - 2005 - Annals of Pure and Applied Logic 136 (3):297-333.
    We investigate operators which take a set X to a set relatively computably enumerable in and above X by studying which such sets X can be so mapped into the Turing degree of K. We introduce notions of nontriviality for such operators, and use these to study which additional properties can be required of sets which can be completed to the jump by given operators of this kind.
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  • 2000 Annual Meeting of the Association for Symbolic Logic.A. Pillay, D. Hallett, G. Hjorth, C. Jockusch, A. Kanamori, H. J. Keisler & V. McGee - 2000 - Bulletin of Symbolic Logic 6 (3):361-396.
  • A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.
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