NAIVE SET THEORY

by PAUL R. HALMOS Professor of Mathematics University of Indiana

VAN NOSTRAND REINHOLD COMPANY New York Cincinnati Toronto London Melbourne

-iii-

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Naive Set Theory
Table of contents

Table of contents

  • Title Page iii
  • Preface v
  • Contents vii
  • Section 1 - The Axiom of Extension 1
  • Section 2 - The Axiom of Specification 4
  • Section 3 - Unordered Pairs 8
  • Section 4 - Unions and Intersections 12
  • Section 5 - Complements and Powers 17
  • Section 6 - Ordered Pairs 22
  • Section 7 - Relations 26
  • Section 8 - Functions 30
  • Section 9 - Families 34
  • Section 10 Inverses and Composites 38
  • Section 11 - Numbers 42
  • Section 12 - The Peano Axioms 46
  • Section 13 - Arithmetic 50
  • Section 14 - Order 54
  • Section 15 - The Axiom of Choice 59
  • Section 16 - Zorn's Lemma 62
  • Section 17 - Well Ordering 66
  • Section 18 - Transfinite Recursion 70
  • Section 19 - Ordinal Numbers 74
  • Section 20 - Sets of Ordinal Numbers 78
  • Section 21 - Ordinal Arithmetic 81
  • Section 22 - The Schröder-Bernstein Theorem 86
  • Section 23 - Countable Sets 90
  • Section 24 - Cardinal Arithmetic 94
  • Section 25 - Cardinal Numbers 99
  • Index 102
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