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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 ord...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York : New York, NY, USA :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1990.
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| Edición: | 3rd ed. |
| Colección: | Studies in logic and the foundations of mathematics ;
v. 73. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- 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. Lindstrm'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