Contents
Preface vi i
0.1. Notatio n vii i
Chapter 1. Elementar y embedding s 1
1.1. Ultrapower s 1
1.2. Tower s o f measures 14
1.3. Tre e representation s (par t I ) 17
1.4. Extender s 2 5
1.5. Woodi n cardinal s 3 0
1.6. Generi c ultrapower s 3 6
1.7. Tree s an d th e nonstationar y idea l 4 6
Chapter 2 . Th e stationar y towe r 4 9
2.1. Generalize d stationarit y 4 9
2.2. Stationar y towe r embedding s 5 1
2.3. Completel y Jonsso n cardinal s 5 5
2.4. Forcin g application s 5 9
2.5. Wellfoundednes s 6 1
2.6. Preservin g Woodi n cardinal s 7 4
2.7. Th e countabl e towe r 7 8
Chapter 3 . Application s 8 5
3.1. Regularit y propertie s an d absolutenes s 8 5
3.2. S^-absolutenes s 9 3
3.3. Tre e representation s (par t II ) 9 7
3.4. Fixin g th e theor y o f the universall y Bair e set s 106
Appendix: Forcin g prerequisite s 123
Bibliography 127
Index 13
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