Set theory for the working mathematician

書誌事項

Set theory for the working mathematician

Krzysztof Ciesielski

(London Mathematical Society student texts, 39)

Cambridge University Press, 1997

  • : hbk
  • : pbk

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注記

Includes bibliographical references (p. 225-227) and index

内容説明・目次

内容説明

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.

目次

  • 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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詳細情報

  • NII書誌ID(NCID)
    BA33102156
  • ISBN
    • 0521594413
    • 9780521594653
  • LCCN
    97010533
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xi, 236 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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