Contents

pp v-vi

Preface

pp vii-viii

Part I - Product forcing

pp 1-1

1 - Forcing and Boolean-valued models

pp 2-6

2 - Properties of the generic extension

pp 7-12

3 - Examples of generic reals

pp 13-22

4 - Product forcing

pp 23-26

5 - Examples of product forcing

pp 27-34

6 - The Lévy collapse

pp 35-37

7 - Product measure forcing

pp 38-42

Part II - Iterated forcing

pp 43-43

1 - Two step iteration

pp 44-49

2 - Finite support iteration

pp 50-52

3 - Martin's Axiom

pp 53-55

4 - Suslin's problem

pp 56-58

5 - Whitehead's problem

pp 59-60

6 - Kaplansky's conjecture

pp 61-66

7 - Countable support iteration

pp 67-72

8 - Borel's conjecture

pp 73-78

Part III - Proper forcing

pp 79-79

1 - Stationary sets

pp 80-88

2 - Infinite games on complete Boolean algebras

pp 89-94

3 - Proper forcing

pp 95-99

4 - Examples of proper forcing

pp 100-102

5 - Iteration of proper forcing

pp 103-110

6 - The Proper Forcing Axiom

pp 111-114

7 - Martin's Maximum

pp 115-125

8 - Well-founded iteration

pp 126-130

Bibliography

pp 131-132