This second edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory, . It provides an exposition of some of the most important results in set theory obtained in the 20th century - the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the second edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It also includes recent developments in the field and numerous exercises, along with the enlarged and entirely updated background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.

• Forward by Dana Scott


• Preface


• List of Problems


• 0: Boolean and Heyting Algebras: The Essentials


• 1: Boolean-Valued Models of Set Theory: First Steps


• 2: Forcing and Some Independence Proofs


• 3: Group Actions on V(B) and the Independence of the Axiom of Choice


• 4: Generic Ultrafilters and Transitive Models of ZFC


• 5: Cardinal Collapsing, Boolean Isomorphism, and Applications to the Theory of Boolean Algebras


• 6: Iterated Boolean Extensions, Matrin's Axiom, and Souslin's Hypothesis


• 7: Boolean-Valued Analysis


• 8: Intuitionistic Set Theory and Heyting-Algebra-Valued Models


• Appendix: Boolean and Heyting Algebra-Valued Models as Categories


• Historical Notes


• Bibliography


• Index of Symbols


• Index of Terms

John L. Bell is a member of the editorial boards of the journals Axiomathes and Philosophia Mathematica. he is Professor of Philosophy at the University of Western Ontario and a Fellow of the Royal Society of Canada.