Fundamentals of Stability Theory Perspectives in Logic Series

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the twelfth publication in the Perspectives in Logic series, John T. Baldwin presents an introduction to first order stability theory, organized around the spectrum problem: calculate the number of models a first order theory T has in each uncountable cardinal. The author first lays the groundwork and then moves on to three sections: independence, dependence and prime models, and local dimension theory. The final section returns to the spectrum problem, presenting complete proofs of the Vaught conjecture for ?-stable theories for the first time in book form. The book provides much-needed examples, and emphasizes the connections between abstract stability theory and module theory.

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.

John T. Baldwin works in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois, Chicago.