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- Finite_model_theory abstract "Finite Model Theory (FMT) is a subarea of model theory (MT). MT is the branch of mathematical logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). FMT is a restriction of MT to interpretations of finite structures, which have a finite universe. Since many central theorems of MT do not hold when restricted to finite structures, FMT is quite different from MT in its methods of proof. Central results of classical model theory that fail for finite structures include the compactness theorem, Gödel's completeness theorem, and the method of ultraproducts for first-order logic (FO). As MT is closely related to mathematical algebra, FMT became an "unusually effective" instrument in computer science. In other words: "In the history of mathematical logic most interest has concentrated on infinite structures....Yet, the objects computers have and hold are always finite. To study computation we need a theory of finite structures." Thus the main application areas of FMT are: descriptive complexity theory, database theory and formal language theory. FMT is mainly about discrimination of structures. The usual motivating question is whether a given class of structures can be described (up to isomorphism) in a given language. For instance, can all cyclic graphs be discriminated (from the non-cyclic ones) by a sentence of first-order logic? This can also be phrased as: is the property "cyclic" FO expressible?↑ ↑".
- Finite_model_theory thumbnail Math_graph_nikos_house_01.gif?width=300.
- Finite_model_theory wikiPageExternalLink fmtpods09.pdf.
- Finite_model_theory wikiPageExternalLink index.html.en.
- Finite_model_theory wikiPageExternalLink slides.pdf.
- Finite_model_theory wikiPageExternalLink shortcourse.pdf.
- Finite_model_theory wikiPageExternalLink 9783540212027-c1.pdf.
- Finite_model_theory wikiPageID "1773596".
- Finite_model_theory wikiPageRevisionID "580649625".
- Finite_model_theory hasPhotoCollection Finite_model_theory.
- Finite_model_theory subject Category:Finite_model_theory.
- Finite_model_theory subject Category:Model_theory.
- Finite_model_theory comment "Finite Model Theory (FMT) is a subarea of model theory (MT). MT is the branch of mathematical logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). FMT is a restriction of MT to interpretations of finite structures, which have a finite universe. Since many central theorems of MT do not hold when restricted to finite structures, FMT is quite different from MT in its methods of proof.".
- Finite_model_theory label "Finite model theory".
- Finite_model_theory label "有限モデル理論".
- Finite_model_theory sameAs Théorie_des_modèles_finis.
- Finite_model_theory sameAs 有限モデル理論.
- Finite_model_theory sameAs m.05vtjb.
- Finite_model_theory sameAs Q5450405.
- Finite_model_theory sameAs Q5450405.
- Finite_model_theory wasDerivedFrom Finite_model_theory?oldid=580649625.
- Finite_model_theory depiction Math_graph_nikos_house_01.gif.
- Finite_model_theory isPrimaryTopicOf Finite_model_theory.
