Immunity Properties and the n-C.E. Hierarchy

Abstract. We extend Post’s programme to finite levels of the Ershov hierarchy of ∆2 sets, and characterise, in the spirit of Post [9], the degrees of the immune and hyperimmune d.c.e. sets. We also show that no properly d.c.e. set can be hh-immune, and indicate how to generalise these results to n-c.e. sets, n>2. 1