Author(s): Rod Downey, Noam Greenberg
Series: Annals of Mathematics Studies 206
Publisher: Princeton University Press
Year: 2020
Language: English
Commentary: preprint
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 <-c.a. degrees
5. Domination properties
Chapter IV. Maximal totally -c.a. degrees
1. Existence of maximal totally -c.a. degrees
2. Limits on further maximality
Chapter V. Presentations of left-c.e. reals
1. Background
2. Presentations of c.e. reals and non-total -c.a. permitting
3. Total -c.a. anti-permitting
Chapter VI. m-topped degrees
1. Totally -c.a. degrees are not m-topped
2. Totally 2-c.a. degrees are not m-topped
3. Totally <-c.a. degrees are not m-topped
Chapter VII. Embeddings of the 1-3-1 lattice
1. Embedding the 1-3-1 lattice
2. Non-embedding critical triples
3. Defeating two gates
4. The general construction
Chapter VIII. Prompt permissions
1. Prompt classes
2. Minimal pairs of separating classes
3. Prompt permission and other constructions
Bibliography
