On the turing degrees of divergence bounded computable reals

Abstract

The d-c.e. (difference of c.e.) and dbc (divergence bounded computable) reals are two important subclasses of Δ20-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 Δ20-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 Δ20 reals are all different. © Springer-Verlag Berlin Heidelberg 2005.