Simple Theories and Hyperimaginaries
eBook - PDF

Simple Theories and Hyperimaginaries

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Simple Theories and Hyperimaginaries

About this book

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.

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Yes, you can access Simple Theories and Hyperimaginaries by Enrique Casanovas in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

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