An Introduction to Independence for Analysts

H. G. Dales; W. H. Woodin

doi:10.1017/CBO9780511662256

Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

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An Introduction to Independence for Analysts

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

preface
pp vii-xiv

1 - Homomorphisms from algebras of continuous functions
pp 1-21

2 - Partial orders, Boolean algebras, and ultraproducts
pp 22-42

3 - Woodin's condition
pp 43-53

4 - Independence in set theory
pp 54-79

5 - Martin's Axiom
pp 80-103

6 - Gaps in ordered sets
pp 104-129

7 - Forcing
pp 130-182

8 - Iterated Forcing
pp 183-228

Bibliography
pp 229-234

Index of notation
pp 235-236

Index
pp 237-241

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An Introduction to Independence for Analysts

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