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December 2008 A characterization of the Δ⁰₂ hyperhyperimmune sets
Roland Sh. Omanadze, Andrea Sorbi
J. Symbolic Logic 73(4): 1407-1415 (December 2008). DOI: 10.2178/jsl/1230396928

Abstract

Let A be an infinite Δ₂⁰ 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 \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K.

Citation

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Roland Sh. Omanadze. Andrea Sorbi. "A characterization of the Δ⁰₂ hyperhyperimmune sets." J. Symbolic Logic 73 (4) 1407 - 1415, December 2008. https://doi.org/10.2178/jsl/1230396928

Information

Published: December 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1161.03026
MathSciNet: MR2467226
Digital Object Identifier: 10.2178/jsl/1230396928

Subjects:
Primary: 03D25, 03D30

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 4 • December 2008
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