Elements of Set Theory

Elements of Set Theory

1st Edition - April 28, 1977

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  • Author: Herbert Enderton
  • eBook ISBN: 9780080570426
  • Hardcover ISBN: 9780122384400

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Description

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.

Readership

Undergraduate students interested in set theory.

Table of 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




Product details

  • No. of pages: 279
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: April 28, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9780080570426
  • Hardcover ISBN: 9780122384400

About the Author

Herbert Enderton

Affiliations and Expertise

University of California, Los Angeles, U.S.A.

Ratings and Reviews

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  • Berin B. Sat Feb 12 2022

    Great book for beginners well-versed

    Great book for beginners well-versed in mathematical logic.

  • Daniel L. Wed May 23 2018

    Excellent book for an intro

    Excellent book for an intro course