Journal of Symbolic Logic 73 (4):1407 - 1415 (2008)

Abstract
Let A be an infinite $\Delta _{2}^{0}$ set and let K be creative: we show that K ≤Q A if and only if K ≤Q1 A. (Here ≤Q denotes Q-reducibility, and ≤Q1 is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x) ∩ Wf(y) = ∅, if x ≠ y.) Using this result we prove that A is hyperhyperimmune if and only if no $\Delta _{2}^{0}$ subset B of A is s-complete. i.e., there is no $\Delta _{2}^{0}$ subset B of A such that K̄ ≤s B, where ≤s denotes s-reducibility, and K̄ denotes the complement of K
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DOI 10.2178/jsl/1230396928
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References found in this work BETA

Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Mathematical Logic Quarterly 5 (7‐13):117-125.
Strong Enumeration Reducibilities.Roland Sh Omanadze & Andrea Sorbi - 2006 - Archive for Mathematical Logic 45 (7):869-912.

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