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The Stationary Tower: Notes on a Course by W. Hugh Woodin
 
Paul B. Larson Miami University, Oxford, OH
The Stationary Tower
eBook ISBN:  978-1-4704-2177-9
Product Code:  ULECT/32.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
The Stationary Tower
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The Stationary Tower: Notes on a Course by W. Hugh Woodin
Paul B. Larson Miami University, Oxford, OH
eBook ISBN:  978-1-4704-2177-9
Product Code:  ULECT/32.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
  • Book Details
     
     
    University Lecture Series
    Volume: 322004; 132 pp
    MSC: Primary 03

    The stationary tower is an important method in modern set theory, invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects.

    Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. By giving complete proofs of all the main theorems and discussing them in context, it is intended that the book will become the standard reference on the stationary tower and its applications to descriptive set theory.

    The first two chapters are taken from a graduate course Woodin taught at Berkeley. The concluding theorem in the course was that large cardinals imply that all sets of reals in the smallest model of set theory (without choice) containing the reals are Lebesgue measurable. Additional sections include a proof (using the stationary tower) of Woodin's theorem that, with large cardinals, the Continuum Hypothesis settles all questions of the same complexity as well as some of Woodin's applications of the stationary tower to the studies of absoluteness and determinacy.

    The book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers. It is also recommended for researchers interested in logic, set theory, and forcing.

    Readership

    Graduate students and research mathematicians interested in logic, set theory, large cardinals, and forcing.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Elementary embeddings
    • Chapter 2. The stationary tower
    • Chapter 3. Applications
    • Appendix: Forcing prerequisites
  • Additional Material
     
     
  • Reviews
     
     
    • It is fantastic that such a book has been written, and even just the fact that somebody has attempted to write this material, in a way that is presented here, deserves an accolade.

      Bulletin of the London Mathematical Society
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 322004; 132 pp
MSC: Primary 03

The stationary tower is an important method in modern set theory, invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects.

Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. By giving complete proofs of all the main theorems and discussing them in context, it is intended that the book will become the standard reference on the stationary tower and its applications to descriptive set theory.

The first two chapters are taken from a graduate course Woodin taught at Berkeley. The concluding theorem in the course was that large cardinals imply that all sets of reals in the smallest model of set theory (without choice) containing the reals are Lebesgue measurable. Additional sections include a proof (using the stationary tower) of Woodin's theorem that, with large cardinals, the Continuum Hypothesis settles all questions of the same complexity as well as some of Woodin's applications of the stationary tower to the studies of absoluteness and determinacy.

The book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers. It is also recommended for researchers interested in logic, set theory, and forcing.

Readership

Graduate students and research mathematicians interested in logic, set theory, large cardinals, and forcing.

  • Chapters
  • Chapter 1. Elementary embeddings
  • Chapter 2. The stationary tower
  • Chapter 3. Applications
  • Appendix: Forcing prerequisites
  • It is fantastic that such a book has been written, and even just the fact that somebody has attempted to write this material, in a way that is presented here, deserves an accolade.

    Bulletin of the London Mathematical Society
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.