The degrees of bi-hyperhyperimmune sets

摘要

We study the degrees of bi-hyperhyperimmune (bi-hhi) sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ?_2~0 function, and equivalently, those that compute a weak 2-generic. These characterizations imply that the collection of bi-hhi Turing degrees is closed upwards.