Elements of Set Theory book cover

Elements of Set Theory

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Audience
Undergraduate students interested in set theory.

Hardbound, 279 Pages

Published: April 1977

Imprint: Academic Press

ISBN: 978-0-12-238440-0

Contents


  • Contents

    Preface

    List of Symbols

    Chapter 1 Introduction

    Baby Set Theory

    Sets-An Informal View

    Classes

    Axiomatic Method

    Notation

    Historical Notes

    Chapter 2 Axioms and Operations

    Axioms

    Arbitrary Unions and Intersections

    Algebra of Sets

    Epilogue

    Review Exercises

    Chapter 3 Relations and Functions

    Ordered Pairs

    Relations

    n-Ary Relations

    Functions

    Infinite Cartesian Products

    Equivalence Relations

    Ordering Relations

    Review Exercises

    Chapter 4 Natural Numbers

    Inductive Sets

    Peano's Postulates

    Recursion on ω

    Arithmetic

    Ordering on ω

    Review Exercises

    Chapter 5 Construction of the Real Numbers

    Integers

    Rational Numbers

    Real Numbers

    Summaries

    Two

    Chapter 6 Cardinal Numbers and the Axiom of Choice

    Equinumerosity

    Finite Sets

    Cardinal Arithmetic

    Ordering Cardinal Numbers

    Axiom of Choice

    Countable Sets

    Arithmetic of Infinite Cardinals

    Continuum Hypothesis

    Chapter 7 Orderings and Ordinals

    Partial Orderings

    Well Orderings

    Replacement Axioms

    Epsilon-Images

    Isomorphisms

    Ordinal Numbers

    Debts Paid

    Rank

    Chapter 8 Ordinals and Order Types

    Transfinite Recursion Again

    Alephs

    Ordinal Operations

    Isomorphism Types

    Arithmetic of Order Types

    Ordinal Arithmetic

    Chapter 9 Special Topics

    Well-Founded Relations

    Natural Models

    Cofinality

    Appendix Notation, Logic, and Proofs

    Selected References for Further Study

    List of Axioms

    Index




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