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Upper semilattice of recursively enumerable sQ-degrees. (English. Russian original) Zbl 0788.03060

Algebra Logic 30, No. 4, 265-271 (1991); translation from Algebra Logika 30, No. 4, 405-413 (1991).
A set \(A\) is called \(sQ\)-reducible to \(B\) if there exist recursive functions \(f\) and \(g\) such that, for all \(x\), \(x \in A\) iff \(W_{f(x)} \subseteq B\) (i.e. \(A \leq_ QB)\) and, for all \(y\), \(y \in W_{f(x)}\) implies \(y \leq g(x)\). The author studies various properties of the upper semilattice of recursively enumerable \(sQ\)-degrees and relationships to abstract complexity properties such as speedability in the sense of M. Blum and I. Marques [J. Symb. Logic 38, 579-593 (1973; Zbl 0335.02024)]. For instance, a density theorem is proven, and relationships with \(wtt\)- and \(T\)-degrees are discussed.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
03D30 Other degrees and reducibilities in computability and recursion theory
03D15 Complexity of computation (including implicit computational complexity)

Citations:

Zbl 0335.02024
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References:

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