Description

Book Synopsis

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.

Trade 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

Table of Contents

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.

Set Theory for the Working Mathematician

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    A Paperback by Krzysztof Ciesielski

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      Book details

      Publisher Cambridge University Press
      Published 28 August 1997
      ISBN-13 9780521594653
      978-0521594653
      ISBN-10 0521594650
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      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.

      Trade 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

      Table of Contents

      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.

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