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.
Author(s): William J. Mitchell, John R. Steel
Series: Lecture Notes in Logic 3
Publisher: Cambridge University Press
Year: 2017
Language: English
Pages: 138
Contents......Page 6
0. Introduction......Page 8
1. Good Extender Sequences......Page 12
2. Fine Structure......Page 17
3. Squashed Mice......Page 35
4. Ultrapowers......Page 41
5. Iteration Trees......Page 54
6. Uniqueness of Wellfounded Branches......Page 65
7. The Comparison Process......Page 76
8. Solidity and Condensation......Page 81
9. Uniqueness of the Next Extender......Page 96
10. Closure under Initial Segment......Page 103
11. The Construction......Page 106
12. Iterability......Page 115
References......Page 132
Index of Definitions......Page 133
Index......Page 135
