Simple Theories and Hyperimaginaries

Enrique Casanovas

• Publisher: Cambridge University Press
• Year: 2011
• Print ISBN:
  9780521119559
• eBook ISBN:
  9781139089081
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Simple Theories and Hyperimaginaries
• Title
• Copyright
• Dedication
• CONTENTS
• PREFACE
• Chapter 1 PRELIMINARIES
• Chapter 2 φ-TYPES, STABILITY AND SIMPLICITY
• Chapter 3 Δ-TYPES AND THE LOCAL RANK D(π, Δ, k)
• Chapter 4 FORKING
• Chapter 5 INDEPENDENCE
• Chapter 6 THE LOCAL RANK CBΔ (π)
• Chapter 7 HEIRS AND COHEIRS
• Chapter 8 STABLE FORKING
• Chapter 9 LASCAR STRONG TYPES
• Chapter 10 THE INDEPENDENCE THEOREM
• Chapter 11 CANONICAL BASES
• Chapter 12 ABSTRACT INDEPENDENCE RELATIONS
• Chapter 13 SUPERSIMPLE THEORIES
• Chapter 14 MORE RANKS
• Chapter 15 HYPERIMAGINARIES
• Chapter 16 HYPERIMAGINARY FORKING
• Chapter 17 CANONICAL BASES REVISITED
• Chapter 18 ELIMINATION OF HYPERIMAGINARIES
• Chapter 19 ORTHOGONALITY AND ANALYSABILITY
• Chapter 20 HYPERIMAGINARIES IN SUPERSIMPLE THEORIES
• REFERENCES
• INDEX