Degrees of Unsolvability
Local and Global Theory

This volume presents a systematic study of the interaction between local and global degree theory.

Manuel Lerman (Author)

9781107168138, Cambridge University Press

Hardback, published 6 April 2017

321 pages, 42 b/w illus.
24.2 x 16.5 x 2.5 cm, 0.68 kg

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the eleventh publication in the Perspectives in Logic series, Manuel Lerman presents a systematic study of the interaction between local and global degree theory. He introduces the reader to the fascinating combinatorial methods of recursion theory while simultaneously showing how to use these methods to prove global theorems about degrees. The intended reader will have already taken a graduate-level course in recursion theory, but this book will also be accessible to those with some background in mathematical logic and a feeling for computability. It will prove a key reference to enable readers to easily locate facts about degrees and it will direct them to further results.

Introduction
Part I. The Structure of the Degrees: 1. Recursive functions
2. Embeddings and extensions of embeddings in the degrees
3. The jump operator
4. High/low hierarchies
Part II. Countable Ideals of Degrees: 5. Minimal degrees
6. Finite distributive lattices
7. Finite lattices
8. Countable usls
Part III. Initial Segments ofD and the Jump Operator: 9. Minimal degrees and high/low hierarchies
10. Jumps of minimal degrees
11. Bounding minimal degrees with recursively enumerable degrees
12. Initial segments of D [0,0']
Appendix A. Coding into structures and theories
Appendix B. lattice tables and representation theorems
References
Notation index
Subject index.

Subject Areas: Mathematical theory of computation [UYA], Functional analysis & transforms [PBKF], Mathematical logic [PBCD]