Degree structures below 0'

This thesis is concerned with various degree structures below 0', varying from Turing degrees to truth-table degrees, from computably enumerable degrees to ∆_2^0 degrees. In Chapter 1, we first provide a general introduction to the development of computability theory in the last few decades, after which, we will present the motivation of our results contained in this thesis. Notation and terminology will be introduced briey at the end of this chapter.DOCTOR OF PHILOSOPHY (SPMS