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A characterization of the \(\Delta _2^0\) hyperhyperimmune sets. (English) Zbl 1161.03026

Using the \(Q\)-reducibility of Tennenbaum and a related \(Q_1\)-subreducibility, the authors prove that if \(A\) is an infinite \(\Delta^0_2\) set and \(K\) is a creative set then \(K \leq_Q A\) if and only if \(K \leq_{Q_1}A\). Applying this, they obtain a new characterization of the hyperhyperimmune sets as those sets without \(S\)-complete \(\Delta^0_2\) subsets.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
03D30 Other degrees and reducibilities in computability and recursion theory
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References:

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[2] On subcreative sets and S-reducibility 39 pp 669– (1974)
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