The density of noncontiguous degrees (Q1312971)

In 1974 L. P. Sasso proved that below any r.e. degree there exists a noncontiguous r.e. degree. After one year, R. E. Ladner and L. P. Sasso improved the result; they proved that below any r.e. degree there exists a low noncontiguous degree. In 1984, Ambos-Spies proved that the class of contiguous degrees is nowhere dense in the set of low degrees. So the noncontiguous degrees are dense in the low r.e. degrees. In this paper, the author shows that all \(p\)-generic degrees are noncontiguous degrees, whence, by Ingrassia's density theorem of \(p\)-generic degrees, the noncontiguous degrees are dense in the r.e. degrees.