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Introduction to Axiomatic Set Theory

  • Textbook
  • © 1971

Overview

Authors:
  1. Gaisi Takeuti

    1. University of Illinois, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Wilson M. Zaring

    1. University of Illinois, USA

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    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
    Download chapter 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

  12. The Axiom of Choice, the Generalized Continuum Hypothesis and Cardinal Arithmetic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 87-101

  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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Keywords

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.

Authors and Affiliations

  • University of Illinois, USA

    Gaisi Takeuti, Wilson M. Zaring

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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