Density of non-p-generic and non-branching r.e. degrees in r.e. low degrees (Q2367847)

The author proves the following Theorem. Let \({\mathbf d}<_ T{\mathbf c}\) be r.e. degrees and let \({\mathbf d}\) be low. Then there exists an r.e. degree \({\mathbf a}\) such that \({\mathbf d}\leq_ T{\mathbf a}\leq_ T{\mathbf c}\) and \({\mathbf a}\) is non-\(p\)-generic and nonbranching. Corollary. Non-\(p\)-generic and nonbranching r.e. degrees are dense in the low r.e. degrees.