The Stationary Tower: Notes on a Course by W. Hugh Woodin
This book is an introduction to the stationary tower, a method that offers a tool for a construction of generic elementary embeddings. H. Woodin invented the method in the 80s. It produces, among other things, some interesting results concerning forcing-absoluteness, the axiom of determinacy and the descriptive set theory, which follow from various assumptions that there is a class of large (Woodin) cardinals. These facts are discussed in the third chapter. The first chapter provides some background material, while the second presents the stationary tower and its basic properties. These two chapters are an adapted version of lecture notes from a graduate set theory course given by H. Woodin at Berkley in 1996. The book is aimed at graduate students and assumes some familiarity with ultrapowers, forcing and constructability. It contains many examples and also a summary of facts from forcing, collected together in the appendix.