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.
Dr Enrique Casanovas is a Professor of Logic and Philosophy of Science in the Department of Logic, History and Philosophy of Science at the University of Barcelona. His research has been published in the Journal of Symbolic Logic, Annals of Pure and Applied Logic and the Journal of Mathematical Logic, among others.
1. Preliminaries; 2. -types, stability and simplicity; 3. -types and the local rank D( , , k); 4. Forking; 5. Independence; 6. The local rank CB ( ); 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.