An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman's fourth problem
Copyright policy )An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman's fourth problem
AbstractWe prove the following algebraic characterization of elementary equivalence: ≡ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if is an (ω1, ω)-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Löwenheim-Skolem theorem for some λ < ωω for theories having ω1 many sentences, then ≡L = ≡ on such structures.
- University of Florence Italy
Model theory of denumerable and separable structures, Categoricity and completeness of theories, equivalence relations between structures, elementary equivalence, Properties of classes of models, Robinson consistency theorem, Lindström-type theorems, Abstract model theory, countable structures of finite type, Interpolation, preservation, definability
Model theory of denumerable and separable structures, Categoricity and completeness of theories, equivalence relations between structures, elementary equivalence, Properties of classes of models, Robinson consistency theorem, Lindström-type theorems, Abstract model theory, countable structures of finite type, Interpolation, preservation, definability
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