Elements of set theory
Author(s)
Bibliographic Information
Elements of set theory
Academic Press, c1977
- : pbk.
Available at 43 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Bibliography: p. 269-270
Includes index
Description and Table of Contents
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.
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 ?
Arithmetic
Ordering on ?
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
by "Nielsen BookData"