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Simple Theories and Hyperimaginaries

Simple Theories and Hyperimaginaries

Part of Lecture Notes in Logic

  • Date Published: September 2011
  • availability: In stock
  • format: Hardback
  • isbn: 9780521119559

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  • 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.

    • Presents a detailed exposition of the topics with full proofs of results
    • Offers a complete presentation of the model theory of hyperimaginaries
    • Provides a self-contained introduction to simple theories
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    Product details

    • Date Published: September 2011
    • format: Hardback
    • isbn: 9780521119559
    • length: 184 pages
    • dimensions: 233 x 155 x 15 mm
    • weight: 0.38kg
    • availability: In stock
  • Table of Contents

    1. Preliminaries
    2. ∂-types, stability and simplicity
    3. Δ-types and the local rank D(π, Δ, 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.

  • Author

    Enrique Casanovas, Universidad de Barcelona
    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.

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