# Fundamentals of Contemporary Set Theory

• Keith J. Devlin
Book

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-viii
2. Keith J. Devlin
Pages 1-34
3. Keith J. Devlin
Pages 35-80
4. Keith J. Devlin
Pages 81-122
5. Keith J. Devlin
Pages 123-148
6. Keith J. Devlin
Pages 149-160
7. Keith J. Devlin
Pages 161-175
8. Back Matter
Pages 176-183

### Introduction

This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.

### Keywords

Area Menge Natural character development form function mathematics minimum proof set set theory sets system time

#### Authors and affiliations

• Keith J. Devlin
• 1
1. 1.University of LancasterLancasterEngland

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-0084-7
• Copyright Information Springer-Verlag New York 1979
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90441-2
• Online ISBN 978-1-4684-0084-7
• Series Print ISSN 0172-5939
• Series Online ISSN 2191-6675