Lecture Notes in Logic, 3

Fine Structure and Iteration Trees

William J. Mitchell and John R. Steel

Year: 2017
ISBN: 9781107169098
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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 of Contents

  • 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.