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  3. Set Theory for the Working Mathematician
  • Cited by 65
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
1997
Online ISBN:
9781139173131
DOI:
https://doi.org/10.1017/CBO9781139173131
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Discrete Mathematics Information Theory and Coding
Series:
London Mathematical Society Student Texts (39)
Information

Book description

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.

Reviews

‘ … 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 Source: Proceedings of the Edinburgh Mathematical Society

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