Introduction to Axiomatic Set Theory / by G. Takeuti, W.M. Zaring.

Format:

Book

Author/Creator:

Takeuti, G., author.

Zaring, W.M., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 1.

Graduate Texts in Mathematics, 2197-5612 ; 1

Language:

English

Subjects (All):

Mathematics.

Mathematics, general.

Local Subjects:

Mathematics, general.

Physical Description:

1 online resource (VII, 251 pages).

Edition:

First edition 1971.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1971.

System Details:

text file PDF

Summary:

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.

Contents:

1 Introduction

2 Language and Logic

3 Equality

4 Classes

5 The Elementary Properties of Classes

6 Functions and Relations

7 Ordinal Numbers

8 Ordinal Arithmetic

9 Relational Closure and the Rank Function

10 Cardinal Numbers

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

12 Models

13 Absoluteness

14 The Fundamental Operations

15 The Gödel Model

16 The Arithmetization of Model Theory

17 Cohen's Method

18 Forcing

19 Languages, Structures, and Models

Problem List

Index of Symbols.

Other Format:

Printed edition:

ISBN:

9781468499155

Access Restriction:

Restricted for use by site license.