Highness, locally noncappability and nonboundings

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Annals of Pure and Applied Logic 164 (5):511-522 (2013)
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Abstract

In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable degree a, there is a high2 r.e. degree c>ac>a witnessing that a is locally noncappable . Theorem 1.1 provides a scheme of obtaining high2 nonboundings , as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc

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10.1016/j.apal.2012.11.008

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References found in this work

Minimal pairs and high recursively enumerable degrees.S. B. Cooper - 1974 - Journal of Symbolic Logic 39 (4):655-660.
Highness and bounding minimal pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.
Degrees which do not bound minimal degrees.Manuel Lerman - 1986 - Annals of Pure and Applied Logic 30 (3):249-276.
The computably enumerable degrees are locally non-cappable.Matthew B. Giorgi - 2004 - Archive for Mathematical Logic 43 (1):121-139.

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