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Fundamentals of Stability Theory

$173.00 (C)

Part of Perspectives in Logic

  • Date Published: March 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107168091

$ 173.00 (C)

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About the Authors
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the twelfth publication in the Perspectives in Logic series, John T. Baldwin presents an introduction to first order stability theory, organized around the spectrum problem: calculate the number of models a first order theory T has in each uncountable cardinal. The author first lays the groundwork and then moves on to three sections: independence, dependence and prime models, and local dimension theory. The final section returns to the spectrum problem, presenting complete proofs of the Vaught conjecture for ω-stable theories for the first time in book form. The book provides much-needed examples, and emphasizes the connections between abstract stability theory and module theory.

    • Contains complete proofs of the Vaught conjecture for ω-stable theories for the first time in book form
    • Provides the first publication of Shelah's infamous example showing the necessity of his methods to solve Vaught's conjecture for the ω-stable theories
    • Emphasizes connections between abstract stability theory and algebra, especially the theory of modules
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    Product details

    • Date Published: March 2017
    • format: Hardback
    • isbn: 9781107168091
    • length: 461 pages
    • dimensions: 240 x 162 x 34 mm
    • weight: 0.88kg
    • contains: 51 b/w illus.
    • availability: Available
  • Table of Contents

    1. Groundwork
    Part I. Independence:
    2. The abstract notion of independence
    3. Forking
    4. Finite equivalence relations, definability, and strong types
    5. Indiscernibles in stable theories
    6. Orthogonality
    7. Rank
    8. Normalization and Teq
    Part II. Dependence and Prime Models:
    9. Atomic and prime models
    10. Freeness and isolation
    Part III. Local Dimension Theory:
    11. Acceptable classes
    12. Regular types
    13. Decomposition theorems and weight
    Part IV. The Number of Models:
    14. The construction of many nonisomorphic models
    15. The width of a theory
    16. The dimensional order property
    17. NDOP: theories without the dimensional order property
    18. Vaught and Morley conjectures for ω-stable countable theories
    Subject index
    Symbol index.

  • Author

    John T. Baldwin, University of Illinois, Chicago
    John T. Baldwin works in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois, Chicago.

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