This is the second volume of a graduate course in set theory. It is aimed at advanced graduate students and at research mathematicians who specialize in fields other than set theory. The volume is intended as a bridge between introductory set theory courses (such as Volume I of the same text) and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. It contains short but rigorous introductions to various set-theoretic techniques that have found numerous applications outside of set theory. Topics covered include: trees, partition calculus, applications of Martin's Axiom and the Diamond-Principle, closed unbounded and stationary sets, measurable cardinals, and the use of elementary submodels. A table of contents and a more detailed list of topics covered are also available at this web site.
Although we think of Volume II as a natural continuation of Volume I, each volume is sufficiently self-contained to be studied separately.
Much of this book is written like a dialogue between the authors and the reader. This is intended to model the practice of creative mathematical thinking, which more often than not takes on the form of an inner dialogue in a mathematician's mind. The authors hope that this format will entice the reader into active participation in discovering the mathematics presented, making the book especially suitable for self-study. The text contains hundreds of carefully selected exercises that will test the reader's understanding of the material.
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