Elements of Set Theory

  • ID: 1760140
  • Book
  • 279 Pages
  • Elsevier Science and Technology
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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.
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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


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Enderton, Herbert B.
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