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Array nonrecursiveness and relative recursive enumerability. (English) Zbl 1269.03044

Author’s abstract: In this paper we prove that a degree \({\mathbf a}\) is array nonrecursive if and only if every degree \({\mathbf b\geq\mathbf a}\) is r.e. in and strictly above another degree. This result answers some questions in [K. Ambos-Spies et al., J. Symb. Log. 74, No. 3, 989–1000 (2009; Zbl 1201.03025)]. We also deduce an interesting corollary that every \(n\)-REA degree has a strong minimal cover if and only if it is array recursive.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
03D28 Other Turing degree structures

Citations:

Zbl 1201.03025
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References:

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[2] M. Cai and R.A. Shore Domination, forcing, array nonrecursiveness and relative recursive enumerablity , Journal of Symbolic Logic, vol. 77(2012), no. 1, pp. 33-48. · Zbl 1269.03045 · doi:10.2178/jsl/1327068690
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