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Lecture Notes in Logic, 39
Simple Theories and Hyperimaginaries


Enrique Casanovas


In the 1990s Kim and Pillay generalized stability, a major model theoretic idea developed by Shelah twenty-five years earlier, to the study of simple theories. This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability, and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability or simplicity of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories.

Year: 2011
Price:$75.00 ISBN-13: 9780521119559
184 pages. Hardcover.
(when ordering, include the discount code ASL2016 to receive the 25% ASL member discount)

Table of Contents

1. Preliminaries
2. ∂-types, stability and simplicity
∆-types and the local rank D(π∆k)
4. Forking
5. Independence
6. The local rank CB∆(π)
7. Heirs and coheirs
8. Stable forking
9. Lascar strong types
10. The independence theorem
11. Canonical bases
12. Abstract independence relations
13. Supersimple theories
14. More ranks
15. Hyperimaginaries
16. Hyperimaginary forking
17. Canonical bases revisited
18. Elimination of hyperimaginaries
19. Orthogonality and analysability
20. Hyperimaginaries in supersimple theories

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