This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
John T. Baldwin works in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois, Chicago.
Inhaltsangabe
Acknowledgements 1. Groundwork Part I. Independence: 2. The abstract notion of independence 3. Forking 4. Finite equivalence relations, definability, and strong types 5. Indiscernibles in stable theories 6. Orthogonality 7. Rank 8. Normalization and Teq Part II. Dependence and Prime Models: 9. Atomic and prime models 10. Freeness and isolation Part III. Local Dimension Theory: 11. Acceptable classes 12. Regular types 13. Decomposition theorems and weight Part IV. The Number of Models: 14. The construction of many nonisomorphic models 15. The width of a theory 16. The dimensional order property 17. NDOP: theories without the dimensional order property 18. Vaught and Morley conjectures for ¿-stable countable theories Bibliography Subject index Symbol index.
Acknowledgements 1. Groundwork Part I. Independence: 2. The abstract notion of independence 3. Forking 4. Finite equivalence relations, definability, and strong types 5. Indiscernibles in stable theories 6. Orthogonality 7. Rank 8. Normalization and Teq Part II. Dependence and Prime Models: 9. Atomic and prime models 10. Freeness and isolation Part III. Local Dimension Theory: 11. Acceptable classes 12. Regular types 13. Decomposition theorems and weight Part IV. The Number of Models: 14. The construction of many nonisomorphic models 15. The width of a theory 16. The dimensional order property 17. NDOP: theories without the dimensional order property 18. Vaught and Morley conjectures for ¿-stable countable theories Bibliography Subject index Symbol index.
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