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A characterization of the δ20 hyperhyperimmune sets

Published online by Cambridge University Press:  12 March 2014

Roland Sh. Omanadze  and
Andrea Sorbi
Roland Sh. Omanadze
Affiliation:
Javakhishvili Tbilisi State University, Tbilisi 0186., Georgia, E-mail: r.omanadze@math.sci.tsu.ge
Andrea Sorbi
Affiliation:
Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, Università di Siena. 53100 Siena, Italy, E-mail: sorbi@unisi.it
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Abstract

Let A be an infinite set and let K be creative: we show that K ≤QA if and only if KA. (Here ≤Q denotes Q-reducibility, and 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 subset B of A is s-complete, i.e., there is no subset B of A such that ≤sB, where ≤s denotes s-reducibility, and denotes the complement of K.

Keywords

Q-reducibilitys-reducibilityhyperhyperimmune set

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1407 - 1415
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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