Simple Theories and Hyperimaginaries

Download or read book Simple Theories and Hyperimaginaries written by Enrique Casanovas and published by Cambridge University Press. This book was released on 2011-06-30 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.