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  • Textbook
  • © 1971

Introduction to Axiomatic Set Theory

Authors:

  1. Gaisi Takeuti

    1. University of Illinois, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Wilson M. Zaring

    1. University of Illinois, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-VII
    PDF

  2. Introduction

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 1-3

  3. Language and Logic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 4-5

  4. Equality

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 6-8

  5. Classes

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 9-13

  6. The Elementary Properties of Classes

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 14-20

  7. Functions and Relations

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 21-31

  8. Ordinal Numbers

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 32-48

  9. Ordinal Arithmetic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 49-62

  10. Relational Closure and the Rank Function

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 63-70

  11. Cardinal Numbers

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 71-86

  13. Models

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 102-111

  14. Absoluteness

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 112-132

  15. The Fundamental Operations

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 133-142

  16. The Gödel Model

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 143-174

  17. The Arithmetization of Model Theory

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 175-195

  18. Cohen’s Method

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 196-202

  19. Forcing

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 203-235

  20. Languages, Structures, and Models

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 236-238
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About this book

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.
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Keywords

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Authors and Affiliations

  • University of Illinois, USA

    Gaisi Takeuti, Wilson M. Zaring

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Bibliographic Information

  • Book Title: Introduction to Axiomatic Set Theory

  • Authors: Gaisi Takeuti, Wilson M. Zaring

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9915-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1971

  • eBook ISBN: 978-1-4684-9915-5Published: 01 December 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: VII, 251

  • Topics: Mathematics, general

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Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

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