Fundamentals of Stability Theory

ISBN-13: 9781107168091 / Angielski / Twarda / 2017 / 461 str.

John T. Baldwin

Opis

This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for omega-stable theories.

Spis treści

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 ω-stable countable theories; Bibliography; Subject index; Symbol index.