Elements of Set Theory
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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
Latest reviews
(Total rating for all reviews)
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