**University Lecture Series**

Volume: 32;
2004;
132 pp;
Softcover

MSC: Primary 03;

Print ISBN: 978-0-8218-3604-0

Product Code: ULECT/32

List Price: $34.00

AMS Member Price: $27.20

MAA Member Price: $30.60

**Electronic ISBN: 978-1-4704-2177-9
Product Code: ULECT/32.E**

List Price: $34.00

AMS Member Price: $27.20

MAA Member Price: $30.60

#### Supplemental Materials

# The Stationary Tower: Notes on a Course by W. Hugh Woodin

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*Paul B. Larson*

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## The Stationary Tower: Notes on a Course by W. Hugh Woodin

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- 01. Notation viii9 free

- Chapter 1. Elementary embeddings 112 free
- Chapter 2. The stationary tower 4960
- Chapter 3. Applications 8596
- Appendix: Forcing prerequisites 123134
- Bibliography 127138
- Index 131142
- Back Cover Back Cover1144