Immunity properties and the n-c.e. hierarchy

Immunity properties and the n-c.e. hierarchy

by B. Afshari, G. Barmpalias and B. S. Cooper

Summary

We extend Posts programme to finite levels of the Ershov hierarchy of $\Delta^0_2$ sets, and characterize, in the spirit of Post, 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 generalize these results to n-c.e. sets for n larger than 2.