ON TRANSFINITE LEVELS OF THE ERSHOV HIERARCHY

Abstract

In this thesis, we study Turing degrees in the context of classical recursion theory. The dissertation is motivated by the \Sigma_1-elementary substructure problem. We consider the problem for transfinite levels of the Ershov hierarchy. The techniques in our results are motivated by two remarkable theorems, Sacks Density Theorem and d.r.e Nondensity Theorem.