Transcription of AN INTRODUCTION TO SET THEORY - …
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AN INTRODUCTION TO SET THEORY - …
AN INTRODUCTION TO SET THEORYP rofessor William A. R. WeissOctober 2, 20082 Contents0 Introduction71 LOST112 FOUND193 The Axioms of Set Theory234 The Natural Numbers315 The Ordinal Numbers416 Relations and Orderings537 Cardinality598 There Is Nothing Real About The Real Numbers659 The Universe7334 CONTENTS10 Reflection7911 Elementary Submodels8912 Constructibility10113 The Axioms of ZFC .. Tentative Axioms .. 118 CONTENTS5 PrefaceThese notes for a graduate course in set THEORY are on their way to be-coming a book. They originated as handwritten notes in a course at theUniversity of Toronto given by Prof. William Weiss. Cynthia Church pro-duced the first electronic copy in December 2002. James Talmage Adamsproduced the copy here in February 2005. Chapters 1 to 9 are close to fi-nal form. Chapters 10, 11, and 12 are quite readable, but should not beconsidered as a final draft.
Contents 0 Introduction 7 1 LOST 11 2 FOUND 19 3 The Axioms of Set Theory 23 4 The Natural Numbers 31 5 The Ordinal Numbers 41 6 Relations and Orderings 53
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