A characterization of the δ20 hyperhyperimmune sets
Roland Sh. Omanadze, Andrea Sorbi · Journal of Symbolic Logic · 2008
Abstract Let A be an infinite set and let K be creative: we show that K ≤QA if and only if K A. (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.