Consequences of Martin's Axiom

D. H. Fremlin

doi:10.1017/CBO9780511896972

'Martin's axiom' is one of the most fruitful axioms which have been devised to show that certain properties are insoluble in standard set theory. It has important 1applications m set theory, infinitary combinatorics, general topology, measure theory, functional analysis and group theory. In this book Dr Fremlin has sought to collect together as many of these applications as possible into one rational scheme, with proofs of the principal results. His aim is to show how straightforward and beautiful arguments can be used to derive a great many consistency results from the consistency of Martin's axiom.

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Consequences of Martin's Axiom

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Acknowledgements
pp vii-viii

Introduction
pp ix-xii

1 - The three cardinals
pp 1-29

2 - When p > ω1
pp 30-110

3 - When mK > ω1
pp 111-173

4 - When m > ω1
pp 174-231

Appendix A - Useful facts
pp 232-287

Appendix B - Consistency results
pp 288-297

Bibliography
pp 298-312

Index of special symbols and abbreviations
pp 313-317

General index
pp 318-325

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Consequences of Martin's Axiom

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