Abstract: We consider sets without subsets of higher m- and tt-degree, that we call m-introimmune and tt-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 Π10-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 tt-introimmune sets.