Highness, locally noncappability and nonboundings

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Abstract

In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable (r.e.) degree a, there is a high2 r.e. degree c>a witnessing that a is locally noncappable (Theorem 1.1). Theorem 1.1 provides a scheme of obtaining high2 nonboundings (Theorem 1.6), as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc.

MSC

03D10
03D20
03D25
03D28

Keywords

Recursively enumerable degrees
Locally noncappable degrees
Nonboundings

Cited by (0)

Stephan is partially supported by NUS grants R252-000-308-112 and R252-000-420-112. Wu is partially supported by AcRF grants RG37/09, M52110101 and MOE2011-T2-1-071 (ARC 17/11, M45110030) from Ministry of Education of Singapore. The authors would like to thank the anonymous referee for many good suggestions for improving the paper.