Axiomatic Set Theory

  • Gaisi Takeuti
  • Wilson M. Zaring

Part of the Graduate Texts in Mathematics book series (GTM, volume 8)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Gaisi Takeuti, Wilson M. Zaring
    Pages 1-1
  3. Gaisi Takeuti, Wilson M. Zaring
    Pages 3-24
  4. Gaisi Takeuti, Wilson M. Zaring
    Pages 25-34
  5. Gaisi Takeuti, Wilson M. Zaring
    Pages 35-46
  6. Gaisi Takeuti, Wilson M. Zaring
    Pages 47-50
  7. Gaisi Takeuti, Wilson M. Zaring
    Pages 51-58
  8. Gaisi Takeuti, Wilson M. Zaring
    Pages 59-63
  9. Gaisi Takeuti, Wilson M. Zaring
    Pages 64-78
  10. Gaisi Takeuti, Wilson M. Zaring
    Pages 79-86
  11. Gaisi Takeuti, Wilson M. Zaring
    Pages 87-101
  12. Gaisi Takeuti, Wilson M. Zaring
    Pages 102-105
  13. Gaisi Takeuti, Wilson M. Zaring
    Pages 106-113
  14. Gaisi Takeuti, Wilson M. Zaring
    Pages 114-120
  15. Gaisi Takeuti, Wilson M. Zaring
    Pages 121-130
  16. Gaisi Takeuti, Wilson M. Zaring
    Pages 131-142
  17. Gaisi Takeuti, Wilson M. Zaring
    Pages 143-147
  18. Gaisi Takeuti, Wilson M. Zaring
    Pages 148-159
  19. Gaisi Takeuti, Wilson M. Zaring
    Pages 160-164
  20. Gaisi Takeuti, Wilson M. Zaring
    Pages 165-168

About this book

Introduction

This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda­ mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.

Keywords

forcing proof set theory

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-8751-0
  • Copyright Information Springer-Verlag New York 1973
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90050-6
  • Online ISBN 978-1-4684-8751-0
  • Series Print ISSN 0072-5285
  • About this book