Lecture Notes in Logic, 8

The Core Model Iterability Problem

John R. Steel

Year: 2017
ISBN: 9781107167964
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Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or ‘core models’, satisfying them. Since Gödel’s pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

Table of Contents

  • Introduction
  1. The construction of K^c
  2. Iterability
  3. Thick classes and universal weasels
  4. The hull and definability properties
  5. The construction of true K
  6. An inductive definition of K
  7. Some applications
  8. Embeddings of K
  9. A general iterability theorem
  • References
  • Index of definitions