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Introduction to Axiomatic Set Theory

  • Gaisi Takeuti
  • Wilson M. Zaring

Part of the Graduate Texts in Mathematics book series (GTM, volume 1)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Gaisi Takeuti, Wilson M. Zaring
    Pages 1-3
  3. Gaisi Takeuti, Wilson M. Zaring
    Pages 4-5
  4. Gaisi Takeuti, Wilson M. Zaring
    Pages 6-8
  5. Gaisi Takeuti, Wilson M. Zaring
    Pages 9-13
  6. Gaisi Takeuti, Wilson M. Zaring
    Pages 14-20
  7. Gaisi Takeuti, Wilson M. Zaring
    Pages 21-31
  8. Gaisi Takeuti, Wilson M. Zaring
    Pages 32-48
  9. Gaisi Takeuti, Wilson M. Zaring
    Pages 49-62
  10. Gaisi Takeuti, Wilson M. Zaring
    Pages 63-70
  11. Gaisi Takeuti, Wilson M. Zaring
    Pages 71-86
  12. Gaisi Takeuti, Wilson M. Zaring
    Pages 102-111
  13. Gaisi Takeuti, Wilson M. Zaring
    Pages 112-132
  14. Gaisi Takeuti, Wilson M. Zaring
    Pages 133-142
  15. Gaisi Takeuti, Wilson M. Zaring
    Pages 143-174
  16. Gaisi Takeuti, Wilson M. Zaring
    Pages 175-195
  17. Gaisi Takeuti, Wilson M. Zaring
    Pages 196-202
  18. Gaisi Takeuti, Wilson M. Zaring
    Pages 203-235
  19. Gaisi Takeuti, Wilson M. Zaring
    Pages 236-238
  20. Back Matter
    Pages 239-251

About this book

Introduction

In 1963, the first author introduced a course in set theory at the Uni­ versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con­ tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub­ ject is compelled to develop the details on his own. However, an in­ structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.

Keywords

arithmetic axiom of choice function logic ordinal set set theory

Authors and affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.University of IllinoisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9915-5
  • Copyright Information Springer-Verlag New York 1971
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-05302-8
  • Online ISBN 978-1-4684-9915-5
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site