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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.
Table des matières
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.
A propos de l'auteur
William J. Mitchell works in the Department of Mathematics at the University of Florida.
Résumé
Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory using the theory of iteration trees. This work builds upon the existing theory of a model of the form L[E], where E is a coherent sequence of extenders.
