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.