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The Core Model Iterability Problem


Part of Lecture Notes in Logic

  • Date Published: March 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107167964

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About the Authors
  • 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. 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.

    • Develops a method for constructing 'core models' that have Woodin cardinals
    • Extends the earlier work of Dodd, Jensen and Mitchell
    • Suitable for advanced students and researchers in set theory
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    Reviews & endorsements

    'Steel's monograph is a masterpiece in terms of both research and exposition. The reviewer ranks it amongst the most significant works in set theory, because of its fundamental advances and broadly applicable new methods. It is required reading for anyone wishing to get up to date on core model theory, and it leads to many beautiful open problems for research.' Ernest Schimmerling, Journal of Symbolic Logic

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    Product details

    • Date Published: March 2017
    • format: Hardback
    • isbn: 9781107167964
    • dimensions: 229 x 152 x 11 mm
    • weight: 0.35kg
    • contains: 1 b/w illus.
    • availability: Available
  • Table of Contents

    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
    Index of definitions.

  • Author

    John R. Steel, University of California, Berkeley
    John R. Steel works in the Department of Mathematics at the University of California, Berkeley.

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