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Highness and local noncappability

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In S. Barry Cooper (ed.), How the World Computes. pp. 203--211 (2012)

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  1. Nonbounding and Slaman triples.Steven D. Leonhardi - 1996 - Annals of Pure and Applied Logic 79 (2):139-163.
    We consider the relationship of the lattice-theoretic properties and the jump-theoretic properties satisfied by a recursively enumerable Turing degree. The existence is shown of a high2 r.e. degree which does not bound what we call the base of any Slaman triple.
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  • The computably enumerable degrees are locally non-cappable.Matthew B. Giorgi - 2004 - Archive for Mathematical Logic 43 (1):121-139.
    We prove that every non-computable incomplete computably enumerable degree is locally non-cappable, and use this result to show that there is no maximal non-bounding computably enumerable degree.
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