Multiple Forcing

T. Jech

doi:10.1017/CBO9780511721168

Multiple Forcing

In this 1987 text Professor Jech gives a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though some results are also included, making the book attractive to set theorists and logicians.

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Multiple Forcing

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Contents

Frontmatter
pp i-iv

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

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Multiple Forcing

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