Skip to main content
SpringerLink
Log in
Book cover

Introduction to Axiomatic Set Theory

  • Textbook
  • © 1982

Overview

Authors:
  1. Gaisi Takeuti

    1. Department of Mathematics, University of Illinois, Urbana, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Wilson M. Zaring

    1. Department of Mathematics, University of Illinois, Urbana, 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)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (19 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

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

  3. Language and Logic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 4-6

  4. Equality

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 7-9

  5. Classes

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 10-14

  6. The Elementary Properties of Classes

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 15-22

  7. Functions and Relations

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 23-34

  8. Ordinal Numbers

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 35-55

  9. Ordinal Arithmetic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 56-72

  10. Relational Closure and the Rank Function

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 73-81

  11. The Axiom of Choice and Cardinal Numbers

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 82-99

  12. Cofinality, the Generalized Continuum Hypothesis, and Cardinal Arithmetic

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 100-110

  13. Models

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 111-120

  14. Absoluteness

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 121-142

  15. The Fundamental Operations

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 143-152

  16. The Gödel Model

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 153-184

  17. Silver Machines

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 185-198

  18. Applications of Silver Machines

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 199-214

  19. Introduction to Forcing

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 215-222

  20. Forcing

    • Gaisi Takeuti, Wilson M. Zaring
    Pages 223-228
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana, 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/10.1007/978-1-4613-8168-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-1-4613-8170-9Published: 12 December 2011

  • eBook ISBN: 978-1-4613-8168-6Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: X, 246

  • Topics: Mathematical Logic and Foundations

Publish with us

Policies and ethics

Back to top

Search

Navigation