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 ∆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 ∆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 ∆0 2 reals are all different.

• Type: Conference
• Year: 2005
• Where: CIE
• Authors: Robert Rettinger, Xizhong Zheng
• Keywords: CIE 2005, Double Witness Technique, Important Subclasses, Nice Analytical Properties