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Model theory /
This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpre...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1993.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 42. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 1 Naming of parts; 1.1 Structures; 1.2 Homomorphisms and substructures; 1.3 Terms and atomic formulas; 1.4 Parameters and diagrams; 1.5 Canonical models; History And Bibliography; 2 Classifying structures; 2.1 Definable subsets; 2.2 Definable classes of structures; 2.3 Some notions from logic; 2.4 Maps and the formulas they preserve; 2.5 Classifying maps by formulas; 2.6 Translations; 2.7 Quantifier elimination; 2.8 Further examples; History and bibliography
- 3 Structures that look alike3.1 Theorems of skolem; 3.2 Back-and-forth equivalence; 3.3 Games for elementary equivalence; 3.4 Closed games; 3.5 Games and infinitary languages; 3.6 Clubs; History and bibliography; 4 Automorphisms; 4.1 Automorphisms; 4.2 Subgroups of small index; 4.3 Imaginary elements; 4.4 Eliminating imaginaries; 4.5 Minimal sets; 4.6 Geometries; 4.7 Almost strongly minimal theories; 4.8 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another
- 5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 6 The first-order case: compactness; 6.1 Compactness for first-order logic; 6.2 Boolean algebras and stone spaces; 6.3 Types; 6.4 Elementary amalgamation; 6.5 Amalgamation and preservation; 6.6 Expanding the language; 6.7 Stability; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method
- History and bibliography8 The existential case; 8.1 Existentially closed structures; 8.2 Two methods of construction; 8.3 Model-completeness; 8.4 Quantifier elimination revisited; 8.5 More on e.c. models; 8.6 Amalgamation revisited; History and bibliography; 9 The Horn case: products; 9.1 Direct products; 9.2 Presentations; 9.3 Word-constructions; 9.4 Reduced products; 9.5 Ultraproducts; 9.6 The feferman-vaught theorem; 9.7 Boolean powers; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models
- 10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 11 Combinatorics; 11.1 Indiscernibles; 11.2 Ehrenfeucht-Mostowski models; 11.3 Em models of unstable theories; 11.4 Nonstandard methods; 11.5 Defining well-orderings; 11.6 Infinitary indiscernibles; History and bibliography; 12 Expansions and categoricity; 12.1 One-cardinal and two-cardinal theorems; 12.2 Categoricity; 12.3 Cohomology of expansions; 12.4 Counting Expansions; 12.5 Relative categoricity; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups