Model Theory book cover

Model Theory

Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.

This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.

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Published: June 1990

Imprint: North-holland

ISBN: 978-0-444-88054-3

Reviews

  • If someone will ask you about the most successful textbook in logical (classical) model theory, your answer may be only one: that is C.C. Chang and H.J. Keisler, Model Theory. This book was published for the first time in 1973. Second revised and enlarged edition appeared in 1977. Now we welcome the third edition of this classic book in classical model theory... The novelties of the third edition are these: a section on recursively saturated models, a section on Lindström's characterization of first order logic, a more extensive treatment of model-completeness and a section on nonstandard universes.
    J. Woleński, Studia Logica

Contents

  • Introduction. What is Model Theory? Model Theory for Sentential Logic. Languages, Models and Satisfaction. Theories and Examples of Theories. Elimination of Quantifiers. Models Constructed from Constants. Completeness and Compactness. Refinements of the Method. Omitting Types and Interpolation Theorems. Countable Models of Complete Theories. Recursively Saturated Models. Lindström's Characterization of First Order Logic. Further Model-Theoretic Constructions. Elementary Extensions and Elementary Chains. Applications of Elementary Chains. Skolem Functions and Indiscernibles. Some Examples. Model Completeness. Ultraproducts. The Fundamental Theorem. Measurable Cardinals. Regular Ultrapowers. Nonstandard Universes. Saturated and Special Models. Saturated and Special Models. Preservation Theorems. Applications of Special Models to the Theory of Definability. Applications to Field Theory. Application to Boolean Algebras. More About Ultraproducts and Generalizations. Ultraproducts Which are Saturated. Direct Products, Reduced Products, and Horn Sentences. Limit Ultrapowers and Complete Extensions. Iterated Ultrapowers. Selected Topics. Categoricity in Power. An Extension of Ramsey's Theorem and Applications; Some Two-Cardinal Theorems. Models of Large Cardinality. Large Cardinals and the Constructible Universe. Appendices: Set Theory. Open Problems in Classical Model Theory. Historical Notes. References. Additional References.

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