Branching in the \({\Sigma^0_2}\)-enumeration degrees: a new perspective (Q938234)
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scientific article; zbMATH DE number 5313048
| Language | Label | Description | Also known as |
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| English | Branching in the \({\Sigma^0_2}\)-enumeration degrees: a new perspective |
scientific article; zbMATH DE number 5313048 |
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Branching in the \({\Sigma^0_2}\)-enumeration degrees: a new perspective (English)
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18 August 2008
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A 1999 paper by \textit{A. Nies} and \textit{A. Sorbi} [Isr. J. Math. 110, 29--59 (1999; Zbl 0924.03080)] showed that every incomplete \(\Sigma_2^0\) enumeration degree can be written as the meet of two incomparable \(\Sigma_2^0\) e-degrees. The present paper arrives at this result by a different route, via the following theorem: For every e-incomplete \(\Sigma_2^0\) set~\(A\), there exists a noncomputable \(\Delta_2^0\) set~\(X\) such that any set simultaneously e-reducible to~\(A\) and Turing reducible to~\(X\) must be computable.
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enumeration reducibility
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semirecursive set
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branching element
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