Immunity properties of the s-degrees
Roland Sh. Omanadze, Andrea Sorbi · Georgian Mathematical Journal · 2010
Abstract We investigate immunity properties of the s-degrees. In particular we show that neither the immune nor the hyperimmune s-degrees are upwards closed since there exist s-degrees a ≤s b such that a is hyperimmune, but b is immune free. We also show that there is no hyperhyperimmune set A such that , where is the complement of the halting set and ≤ŝ denotes the finite-branch version of s-reducibility.