Array nonrecursiveness and relative recursive enumerability

Journal of Symbolic Logic 77 (1):21-32 (2012)
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Abstract

In this paper we prove that a degree a is array nonrecursive (ANR) if and only if every degree b ≥ a is r.e. in and strictly above another degree (RRE). This result will answer some questions in [ASDWY]. We also deduce an interesting corollary that every n-REA degree has a strong minimal cover if and only if it is array recursive

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