Admissible Sets and Structures

This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

Jon Barwise (Author)

9781107168336, Cambridge University Press

Hardback, published 2 March 2017

408 pages, 21 b/w illus.
24 x 16.2 x 3.2 cm, 0.8 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. Admissible set theory is a major source of interaction between model theory, recursion theory and set theory, and plays an important role in definability theory. In this volume, the seventh publication in the Perspectives in Logic series, Jon Barwise presents the basic facts about admissible sets and admissible ordinals in a way that makes them accessible to logic students and specialists alike. It fills the artificial gap between model theory and recursion theory and covers everything the logician should know about admissible sets.

Introduction
Part I. The Basic Theory: 1. Admissible set theory
2. Some admissible sets
3. Countable fragments of L??
4. Elementary results on HYPM
Part II. The Absolute Theory: 5. The recursion theory of ?1, predicates on admissible sets
6. Inductive definitions
Part III. Towards a General Theory: 7. More about L??
8. Strict ?11 predicates and Koenig principles
Appendix. Nonstandard compactness arguments and the admissible cover
References
Index of notation
Subject index.

Subject Areas: Mathematical theory of computation [UYA], Set theory [PBCH], Mathematical logic [PBCD]