Discovering Modern Set Theory Ii - Set-Theoric Tools For Every Mathematician

This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle ($\diamond$), and the use of elementary submodels. Great care has been taken to motivate the concepts and theorems presented. The book is written as a dialogue with the reader. The presentation is interspersed with numerous exercises. The authors wish to entice readers into active participation in discovering the mathematics presented, making the book particularly suitable for self-study. Each topic is presented rigorously and in considerable detail. Carefully planned exercises lead the reader to active mastery of the techniques presented. Suggestions for further reading are given. Volume II can be read independently of Volume I.