Degrees of sets having no subsets of higher m- and t t-degree

Abstract

We consider sets without subsets of higher m- and t t-degree, that we call m-introimmune and t t-introimmune sets respectively. We study how they are distributed in partially ordered degree structures. We show that: each computably enumerable weak truth-table degree contains m-introimmune Π 1 0 -sets; each hyperimmune degree contains bi-m-introimmune sets. Finally, from known results we establish that each degree a with a ′ ⩾ 0 ″ covers a degree containing t t-introimmune sets.