AN INTRODUCTION TO SET THEORY
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 10 Reflection
CONTENTS 79
11 Elementary Submodels
89
12 Constructibility
101
13 Appendices
117
.1 The Axioms of ZFC . . . . . . . . . . . . . . . . . . . . . . . . 117
.2 Tentative Axioms . . . . . . . . . . . . . . . . . . . . . . . . . 118
CONTENTS
5
Preface
These notes for a graduate course in set theory are on their way to becoming a book. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Cynthia Church produced the first electronic copy in December 2002. James Talmage Adams produced the copy here in February 2005. Chapters 1 to 9 are close to final form. Chapters 10, 11, and 12 are quite readable, but should not be considered as a final draft. One more chapter will be added.
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