On the turing degrees of divergence bounded computable reals

The d-c.e. (difference of c.e.) and dbc (divergence bounded computable) reals are two important subclasses of Delta(0)(2)-reals which have very interesting computability-theoretical as well as very nice analytical properties. Recently, Downey, Wu and Zheng [2] have shown by a double witness technique that not every Delta(0)(2)-Turing degree contains a d-c.e. real. In this paper we show that the classes of Turing degrees of d-c.e., dbc and Delta(0)(2) reals are all different.