Dedication

pp v-vi

Contents

pp vii-x

Preface

pp xi-xiv

Part I - Let’s Be Independent

pp 1-2

1 - Introduction

pp 3-4

2 - Axiomatic Systems

pp 5-7

3 - Zermelo–Fraenkel Axioms and the Axiom of Choice

pp 8-16

4 - Well Orderings and Ordinals

pp 17-25

5 - Cardinals

pp 26-28

6 - Models and Independence

pp 29-31

7 - Some Class Models of ZFC

pp 32-49

8 - Forcing

pp 50-60

9 - Violating CH

pp 61-64

Part II - What is New in Set Theory

pp 65-66

10 - Introduction to Part Two

pp 67-67

11 - Classical Extensions

pp 68-70

12 - Iterated Forcing and Martin’s Axiom

pp 71-78

13 - Some More Large Cardinals

pp 79-84

14 - Limitations of Martin’s Axiom and Countable Supports

pp 85-89

15 - Proper Forcing and PFA

pp 90-103

16 - N2 and other Successors of Regulars

pp 104-125

17 - Singular Cardinal Hypothesis and Some PCF

pp 126-132

18 - Forcing at Singular Cardinals and Their Successors

pp 133-136

References

pp 137-143

Index

pp 144-147