The distribution of the generic recursively enumerable degrees

Abstract

Summary. In this paper we investigate problems about densities of e-generic, sgeneric and p-generic degrees. We, in particular, show that all p-generic degrees are non-branching, which answers an open question by Jockusch who asked: whether all s-generic degrees are non-branching and refutes a conjecture of Ingrassia; the set of degrees containing r.e. p-generic sets is the same as the set of r.e. degrees containing an r.e. non-antoreducible set.