Elements of Set Theory
Published on 23. May 1977
Book
Hardback
296 pages
978-0-12-238440-0 (ISBN)
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.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Undergraduate students interested in set theory.
Dimensions
Height: 236 mm
Width: 160 mm
Thickness: 27 mm
Weight
635 gr
ISBN-13
978-0-12-238440-0 (9780122384400)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
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Content
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
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