Advertisement

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-ix
  2. Gaisi Takeuti, Wilson M. Zaring
    Pages 1-3
  3. Gaisi Takeuti, Wilson M. Zaring
    Pages 4-6
  4. Gaisi Takeuti, Wilson M. Zaring
    Pages 7-9
  5. Gaisi Takeuti, Wilson M. Zaring
    Pages 10-14
  6. Gaisi Takeuti, Wilson M. Zaring
    Pages 15-22
  7. Gaisi Takeuti, Wilson M. Zaring
    Pages 23-34
  8. Gaisi Takeuti, Wilson M. Zaring
    Pages 35-55
  9. Gaisi Takeuti, Wilson M. Zaring
    Pages 56-72
  10. Gaisi Takeuti, Wilson M. Zaring
    Pages 73-81
  11. Gaisi Takeuti, Wilson M. Zaring
    Pages 82-99
  12. Gaisi Takeuti, Wilson M. Zaring
    Pages 111-120
  13. Gaisi Takeuti, Wilson M. Zaring
    Pages 121-142
  14. Gaisi Takeuti, Wilson M. Zaring
    Pages 143-152
  15. Gaisi Takeuti, Wilson M. Zaring
    Pages 153-184
  16. Gaisi Takeuti, Wilson M. Zaring
    Pages 185-198
  17. Gaisi Takeuti, Wilson M. Zaring
    Pages 199-214
  18. Gaisi Takeuti, Wilson M. Zaring
    Pages 215-222
  19. Gaisi Takeuti, Wilson M. Zaring
    Pages 223-228
  20. Back Matter
    Pages 229-246

About this book

Introduction

In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con­ sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were 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 high­ lighted, and second, the student who wishes to master the subject is com­ pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text.

Keywords

Cardinal number arithmetic axiom of choice bridge class development forcing object set set theory time university

Authors and affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8168-6
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8170-9
  • Online ISBN 978-1-4613-8168-6
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site