Set Theory for the Working Mathematician

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Krzysztof Ciesielski (Author)

9780521594653, Cambridge University Press

Paperback, published 28 August 1997

252 pages
22.9 x 15.2 x 1.5 cm, 0.345 kg

' … the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.' Ian Tweddle, Proceedings of the Edinburgh Mathematical Society

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

Part I. Basics of Set Theory: 1. Axiomatic set theory
2. Relations, functions and Cartesian product
3. Natural, integer and real numbers
Part II. Fundamental Tools of Set Theory: 4. Well orderings and transfinite induction
5. Cardinal numbers
Part III. The Power of Recursive Definitions: 6. Subsets of Rn
7. Strange real functions
Part IV. When Induction is Too Short: 8. Martin's axiom
9. Forcing
Part V. Appendices: A. Axioms of set theory
B. Comments on forcing method
C. Notation.

Subject Areas: Set theory [PBCH]