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Naive Set Theory

  • Book
  • © 1974

Overview

Authors:
  1. Paul R. Halmos

    1. Department of Mathematics, Santa Clara University, Santa Clara, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. The Axiom of Extension

    • Paul R. Halmos
    Pages 1-3

  3. The Axiom of Specification

    • Paul R. Halmos
    Pages 4-7

  4. Unordered Pairs

    • Paul R. Halmos
    Pages 8-11

  5. Unions and Intersections

    • Paul R. Halmos
    Pages 12-16

  6. Complements and Powers

    • Paul R. Halmos
    Pages 17-21

  7. Ordered Pairs

    • Paul R. Halmos
    Pages 22-25

  8. Relations

    • Paul R. Halmos
    Pages 26-29

  9. Functions

    • Paul R. Halmos
    Pages 30-33

  10. Families

    • Paul R. Halmos
    Pages 34-37

  11. Inverses and Composites

    • Paul R. Halmos
    Pages 38-41

  12. Numbers

    • Paul R. Halmos
    Pages 42-45

  13. The Peano Axioms

    • Paul R. Halmos
    Pages 46-49

  14. Arithmetic

    • Paul R. Halmos
    Pages 50-53

  15. Order

    • Paul R. Halmos
    Pages 54-58

  16. The Axiom of Choice

    • Paul R. Halmos
    Pages 59-61

  17. Zorn’s Lemma

    • Paul R. Halmos
    Pages 62-65

  18. Well Ordering

    • Paul R. Halmos
    Pages 66-69

  19. Transfinite Recursion

    • Paul R. Halmos
    Pages 70-73

  20. Ordinal Numbers

    • Paul R. Halmos
    Pages 74-77
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Keywords

About this book

Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set­ theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

Reviews

From the reviews:

“This book is a very specialized but broadly useful introduction to set theory. It is aimed at ‘the beginning student of advanced mathematics’ … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics … .” (Allen Stenger, The Mathematical Association of America, September, 2011)

Authors and Affiliations

  • Department of Mathematics, Santa Clara University, Santa Clara, USA

    Paul R. Halmos

Bibliographic Information

  • Book Title: Naive Set Theory

  • Authors: Paul R. Halmos

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1645-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1974

  • Hardcover ISBN: 978-0-387-90092-6Published: 16 January 1998

  • Softcover ISBN: 978-0-387-90104-6Published: 12 January 2014

  • eBook ISBN: 978-1-4757-1645-0Published: 27 November 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: VII, 104

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Mathematical Logic and Foundations

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