Model Theory

3rd ed.
ISBN: 978-0-444-88054-3
Verlag: Elsevier Science & Technology

Buch, Englisch

Reihe: Studies in Logic and the Foundations of Mathematics

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.

Inhaltsverzeichnis

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.