The d.r.e wtt-Degrees are Dense

Abstract

© 2019, Springer Nature Switzerland AG. We prove in this paper that the d.r.e. wtt-degrees are dense, improving a result of Wu and Yamaleev. Our result is a direct generalization of Ladner and Sasso’s splitting theorem for r.e. wtt-degrees. One essential feature of our construction is that the Lachlan sets are used as a help to obtain more information of d.r.e. sets.