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AN INTRODUCTION TO SET THEORY


Professor William A. R. Weiss


October 2, 2008

,2

,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


7 Cardinality 59


8 There Is Nothing Real About The Real Numbers 65


9 The Universe 73

3

, 4 CONTENTS

10 Reflection 79


11 Elementary Submodels 89


12 Constructibility 101


13 Appendices 117

.1 The Axioms of ZFC . . . . . . . . . . . . . . . . . . . . . . . . 117

.2 Tentative Axioms . . . . . . . . . . . . . . . . . . . . . . . . . 118