## Manual of axiomatic set theory |

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### Contents

Elementary set theory | 1 |

The axiom of choice | 17 |

Ordinal and cardinal arithmetic | 35 |

Copyright | |

2 other sections not shown

### Common terms and phrases

a e ft Axiom of Choice Axiomatic Set Theory called canonical mapping Cartesian product cofinal Corollary Definition 1.3 definitions and theorems denoted disjoint union equipotent equivalence relation example exists a function exists a set f with domain family of cardinals following definition formulate function f iff card iff there exists iff xRy inaccessible cardinal indexed infinite cardinal initial ordinals isomorphic least element Let Ah iel Let F Let G limit ordinal maximal element natural numbers nonempty sets OAXC OGCH operation of type ord(Y ordinal cardinal ordinal numbers ordinal operation partial ordering pr2f predecessor Proof outline proper class properties prove real numbers S{Ah iel saturated segment set of ordinals singular subclass successor system of representatives Theorem Theorem 20 Theorem 74 totally ordered QOS totally ordered subset transfinite induction well-ordered set Well-Ordering Principle Zorn's Lemma