Contents Introduction vii Part 1. Quasiminimal Excellence and Complex Exponentiation 1 Chapter 1. Combinatorial Geometries and Infinitary Logics 3 1.1. Combinatorial Geometries 3 1.2. Infinitary Logic 4 Chapter 2. Abstract Quasiminimality 7 Chapter 3. Covers of the Multiplicative Group of 17 Part 2. Abstract ElementaryClasses 25 Chapter 4. Abstract Elementary Classes 27 Chapter 5. Two Basic Results about 𝐿𝜔 1 ,𝜔 (𝑄) 39 5.1. Non-definability of Well-order in 𝐿𝜔 1 ,𝜔 (𝑄) 39 5.2. The Number of Models in 𝜔1 41 Chapter 6. Categoricity Implies Completeness 45 6.1. Completeness 45 6.2. Arbitrarily Large Models 50 6.3. Few Models in Small Cardinals 52 6.4. Categoricity and Completeness for 𝐿𝜔 1 ,𝜔 (𝑄) 54 Chapter 7. A Model in ℵ2 57 Part 3. Abstract ElementaryClasses with ArbitrarilyLarge Models 63 Chapter 8. Galois types, Saturation, and Stability 67 Chapter 9. Brimful Models 73 Chapter 10. Special, Limit and Saturated Models 75 Chapter 11. Locality and Tameness 83 Chapter 12. Splitting and Minimality 91 Chapter 13. Upward Categoricity Transfer 99 Chapter 14. Omitting Types and Downward Categoricity 105 v
Previous Page Next Page