This monograph lays the foundations for the theory of canonical inner models of set theory which are large enough to satisfy the statement "There is a Woodin cardinal". It does so by combining Jensen's fine structure models, already useful in the study of smaller inner models, with the theory of iteration trees and Woodin cardinals developed recently by Martin and Steel. The resulting theory is a powerful tool in studying the structure of models of set theory. The main result in this monograph is the construction, given the existence of a Woodin cardinal, of an L-like inner model containing a Woodin cardinal and satisfying the generalized continuum hypothesis, but its real significance is as an indispensable tool for further work with large cardinals in set theory.
Author(s): William J. Mitchell, John R. Steel
Series: Lecture Notes in Logic 3
Edition: 1
Publisher: Springer
Year: 1994
Language: English
Pages: 138
Contents......Page 7
0. Introduction......Page 9
1. Good Extender Sequences......Page 13
2. Fine Structure......Page 18
Skolem terms and projecta......Page 21
Hulls......Page 23
Solid parameters......Page 29
Universal parameters......Page 30
3. Squashed Mice......Page 36
Hulls......Page 40
Premice......Page 41
4. Ultrapowers......Page 42
Relations to Dodd-Jensen......Page 48
5. Iteration Trees......Page 55
Embeddings of iteration trees......Page 60
6. Uniqueness of Wellfounded Branches......Page 66
7. The Comparison Process......Page 77
8. Solidity and Condensation......Page 82
9. Uniquenss of the Next Extender......Page 97
10. Closure under Initial Segment......Page 104
11. The Construction......Page 107
12. Iterability......Page 116
References......Page 133
Index of Definitions......Page 134
Index......Page 136
