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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
Table of Contents
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Front/Back Matter
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