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 𝐿𝜔1,𝜔(𝑄) 39
5.1. Non-definability of Well-order in 𝐿𝜔1,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 𝐿𝜔1,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
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