Fundamentals of Stability Theory

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

John T. Baldwin (Author)

9781107168091, Cambridge University Press

Hardback, published 2 March 2017

461 pages, 51 b/w illus.
24 x 16.2 x 3.4 cm, 0.88 kg

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 ?-stable countable theories
Bibliography
Subject index
Symbol index.

Subject Areas: Differential calculus & equations [PBKJ], Algebra [PBF], Mathematical logic [PBCD]