Set Theory for the Working Mathematician: Krzysztof Ciesielski: 39 (London Mathematical Society Student Texts, Series Number 39) - Softcover

Ciesielski, Krzysztof

Softcover

ISBN 10: 0521594650 ISBN 13: 9780521594653

Publisher: Cambridge University Press, 1997

Synopsis

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.

About this title

Review

' ... 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

Book Description

This text concentrates on the typical methods of modern set theory: transfinite induction, Zorn's Lemma, the Continuum Hypothesis, Martin's Axiom, the Diamond Principle and elements of forcing. It supplies students and researchers with the tools most applicable to other areas of pure mathematics, such as abstract geometry, real analysis, topology, and algebra.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1997
• ISBN 10: 0521594650
• ISBN 13: 9780521594653
• Binding: Paperback
• Language: English
• Number of pages: 252