A Hierarchy of Turing Degrees : A Transfinite Hierarchy of Lowness Notions in the Computably Enumerable Degrees, Unifying Classes, and Natural Definability

Contents Chapter I. Introduction 1. Historical context 2. Background: unifying constructions and natural definability 3. Toward the hierarchy of totally -c.a. degrees 4. The contents of this monograph 5. An application to admissible computability 6. Notation and general definitions Chapter II. -c.a. functions 1. R-c.a. functions 2. Canonical well-orderings and strong notations 3. Weak truth-table jumps and -c.a. sets and functions Chapter III. The hierarchy of totally -c.a. degrees 1. Totally R-c.a. degrees 2. The first hierarchy theorem: totally -c.a. degrees 3. A refinement of the hierarchy: uniformly totally -c.a. degrees 4. Another refinement of the hierarchy: totally