Computably enumerable Turing degrees and the meet property (Q2790280)

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scientific article; zbMATH DE number 6549239
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Computably enumerable Turing degrees and the meet property
scientific article; zbMATH DE number 6549239

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    Computably enumerable Turing degrees and the meet property (English)
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    3 March 2016
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    recursively enumerable sets
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    meet property
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    In [\textit{S.B. Cooper} and \textit{R.L. Epstein}, Ann. Pure Appl. Logic 34, No. 1, 15--32 (1987; Zbl 0629.03016)], Corollary 1, the following result is obtained: for every low c.e. degree \({\mathbf a}>{\mathbf 0}\) and for every c.e. degree \({\mathbf b}\) with \({\mathbf 0}<{\mathbf b}<{\mathbf a}\) there exists a minimal degree \({\mathbf m}<{\mathbf a}\) such that \({\mathbf m}\not\leq{\mathbf b}\). In the present interesting paper, the authors strengthen the above result: for every c.e. degree \({\mathbf a}>{\mathbf 0}\) and for every degree \({\mathbf b}<{\mathbf a}\), there is a minimal degree \({\mathbf m}<{\mathbf a}\) such that \({\mathbf m}\not\leq{\mathbf b}\). This shows that every c.e. degree has the meet property, which was a long standing open question.
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