Fine Structure and Iteration Trees

This book constructs an inner model with a Woodin cardinal and develops its fine structure theory using the theory of iteration trees.

William J. Mitchell (Author), John R. Steel (Author)

9781107169098, Cambridge University Press

Hardback, published 2 March 2017

136 pages, 1 b/w illus.
22.9 x 15.2 x 1.1 cm, 0.3 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 third publication in the Lecture Notes in Logic series, Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory. This work builds upon the existing theory of a model of the form L[E], where E is a coherent sequence of extenders, and relies upon the fine structure theory of L[E] models with strong cardinals, and the theory of iteration trees and 'backgrounded' L[E] models with Woodin cardinals. This work is what results when fine structure meets iteration trees.

Introduction
1. Good extender sequences
2. Fine structure
3. Squashed mice
4. Ultrapowers
5. Iteration trees
6. Uniqueness of wellfounded branches
7. The comparison process
8. Solidarity and condensation
9. Uniqueness of the next extender
10. Closure under initial segment
11. The construction
12. Iterability
References
Index of definitions
Index.

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