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 1 4 1.3. Tre e representation s (par t I ) 1 7 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 10 6 Appendix: Forcin g prerequisite s 12 3 Bibliography 12 7 Index 13 1
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