Professor Jech gives here 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 recent results are also included, making the book attractive to set theorists and logicians.
Author(s): T. Jech
Series: Cambridge Tracts in Mathematics
Publisher: CUP
Year: 1986
Language: English
Pages: 145
Cover......Page 1
Cambridge Tracts in Mathematics 88......Page 2
Multiple forcing......Page 4
Goto 4 /FitH 555521266599......Page 5
Contents......Page 6
Preface......Page 8
Part I Product forcing......Page 10
1 Forcing and Boolean-valued models......Page 11
2 Properties of the generic extension......Page 16
3 Examples of generic reals......Page 22
4 Product forcing......Page 32
5 Examples of product forcing......Page 36
6 The Levy collapse......Page 44
7 Product measure forcing......Page 47
Part II Iterated forcing......Page 52
1 Two step iteration......Page 53
2 Finite support iteration......Page 59
3 Martin's Axiom......Page 62
4 Suslin's problem......Page 65
5 Whitehead's problem......Page 68
6 Kaplansky's conjecture......Page 70
7 Countable support iteration......Page 76
8 Borel's conjecture......Page 82
Part III Proper forcing......Page 88
1 Stationary sets......Page 89
2 Infinite games on complete Boolean algebras......Page 98
3 Proper forcing......Page 104
4 Examples of proper forcing......Page 109
5 Iteration of proper forcing......Page 112
6 The Proper Forcing Axiom......Page 120
7 Martin's Maximum......Page 124
8 Well-founded iteration......Page 135
Bibliography......Page 140
Index of symbols......Page 142
Subject index......Page 143
Author index......Page 145
