Set Theory and the Continuum Problem
Melvin Fitting Professor, Mathematics, Professor, Computer Science, Professor, Philosophy
Revised and updated from the 1996 edition, this volume is a lucid, elegant, and complete survey of set theory drawn from the authors' substantial teaching experience. The book is intended to provide the reader with a complete foundation in modern set theory, explaining how the subject is axiomatized and the role of the axiom of choice, and elucidating ordinal and cardinal numbers, constructible sets, and forcing. The first of three parts focuses on axiomatic set theory, examining problems related to size comparisons between infinite sets, basics of class theory, and natural numbers, as well as Smullyan's double induction principle, super induction, ordinal numbers, order isomorphism and transfinite recursion, and the axiom of foundation and cardinals. The second part addresses Mostowski-Shepherdson mappings, reflection principles, constructible sets and constructibility, and the continuum hypothesis. The text concludes with an extensive exploration of forcing and independence results.
Published April 2010