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Categoricity

About this Title

John T. Baldwin, University of Illinois at Chicago, Chicago, IL

Publication: University Lecture Series
Publication Year: 2009; Volume 50
ISBNs: 978-0-8218-4893-7 (print); 978-1-4704-1645-4 (online)
DOI: https://doi.org/10.1090/ulect/050
MathSciNet review: MR2532039
MSC: Primary 03C48; Secondary 03C30, 03C45, 03C52, 03C60

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Table of Contents

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Front/Back Matter

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Part 1. Quasiminimal excellence and complex exponentiation

• Chapter 1. Combinatorial geometries and infinitary logics
• Chapter 2. Abstract quasiminimality
• Chapter 3. Covers of the multiplicative group of $\mathbb {C}$

Part 2. Abstract elementary classes

• Chapter 4. Abstract elementary classes
• Chapter 5. Two basic results about $L_{\omega _1,\omega }(Q)$
• Chapter 6. Categoricity implies completeness
• Chapter 7. A model in $\aleph _2$

Part 3. Abstract elementary classes with arbitrarily large models

• Chapter 8. Galois types, saturation, and stability
• Chapter 9. Brimful models
• Chapter 10. Special, limit and saturated models
• Chapter 11. Locality and tameness
• Chapter 12. Splitting and minimality
• Chapter 13. Upward categoricity transfer
• Chapter 14. Omitting types and downward categoricity
• Chapter 15. Unions of saturated models
• Chapter 16. Life without amalgamation
• Chapter 17. Amalgamation and few models

Part 4. Categoricity in $L_{\omega _1,\omega }$

• Chapter 18. Atomic AEC
• Chapter 19. Independence in $\omega$-stable classes
• Chapter 20. Good systems
• Chapter 21. Excellence goes up
• Chapter 22. Very few models implies excellence
• Chapter 23. Very few models implies amalgamation over pairs
• Chapter 24. Excellence and *-excellence
• Chapter 25. Quasiminimal sets and categoricity transfer
• Chapter 26. Demystifying non-excellence
• Appendix A. Morley’s omitting types theorem
• Appendix B. Omitting types in uncountable models
• Appendix C. Weak diamonds
• Appendix D. Problems