Set Theory

During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees.
Audience: This book will be of interest to graduate students and researchers in foundational problems of mathematics.

Forcing axioms. - Large cardinal properties of small cardinals. - Countable length Ramsey games. - Weak forms of the axiom of choice and partitions of infinite sets. - A taste of proper forcing. - Applications of ? -functions. - Models as side conditions. - An ordinal partition from a scale. - A picaresque approach to set theory genealogy. - Recurrent points and hyperarithmetic sets. - A tree-arrowing graph. - A Hollow Shell: Covering Lemmas Without a Core. - Partition properties for reals. - Combinatorial set theory and inner models. - Definable ideals and gaps in their quotients.