Skip to main content
SpringerLink
Log in

An Outline of Set Theory

  • Book
  • © 1986

Overview

Authors:
  1. James M. Henle

    1. Department of Mathematics, Smith College, Northampton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Problem Books in Mathematics (PBM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (31 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    1. Introduction

      • James M. Henle
      Pages 1-4

  3. Projects

    1. Front Matter

      Pages 5-5
      Download chapter PDF

    2. Logic and Set Theory

      • James M. Henle
      Pages 7-13

    3. The Natural Numbers

      • James M. Henle
      Pages 15-19

    4. The Integers

      • James M. Henle
      Pages 21-22

    5. The Rationals

      • James M. Henle
      Pages 23-24

    6. The Real Numbers

      • James M. Henle
      Pages 25-26

    7. The Ordinals

      • James M. Henle
      Pages 27-32

    8. The Cardinals

      • James M. Henle
      Pages 33-36

    9. The Universe

      • James M. Henle
      Pages 37-40

    10. Choice and Infinitesimals

      • James M. Henle
      Pages 41-44

    11. Goodstein’s Theorem

      • James M. Henle
      Pages 45-48

  4. Suggestions

    1. Front Matter

      Pages 49-49
      Download chapter PDF

    2. Logic and Set Theory

      • James M. Henle
      Pages 51-53

    3. The Natural Numbers

      • James M. Henle
      Pages 55-56

    4. The Integers

      • James M. Henle
      Pages 57-58

    5. The Rationals

      • James M. Henle
      Pages 59-61

    6. The Real Numbers

      • James M. Henle
      Pages 63-66

    7. The Ordinals

      • James M. Henle
      Pages 67-70
Back to top

Keywords

About this book

This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em­ phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea­ soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio­ neers.

Authors and Affiliations

  • Department of Mathematics, Smith College, Northampton, USA

    James M. Henle

Bibliographic Information

  • Book Title: An Outline of Set Theory

  • Authors: James M. Henle

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4613-8680-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1986

  • Softcover ISBN: 978-0-387-96368-6Published: 10 October 1986

  • eBook ISBN: 978-1-4613-8680-3Published: 06 December 2012

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: VIII, 146

  • Topics: Mathematical Logic and Foundations

Publish with us

Policies and ethics

Back to top

Search

Navigation