The Abstract Compactness Theorem revisited
نویسنده
چکیده
The Abstract Compactness Theorem of Makowsky and Shelah for model theoretic logics is shown to be an immediate consequence of a general characterization of topological spaces having [ ; ]-compact products, when applied to spaces of structures endowed with the natural topology induced by the de nable classes of a logic L. In this context, the notion of an ultra lter U being related to L corresponds to U-compactness of theses spaces. The given characterization of topological productive [ ; ]-compactness may have independent interest since it generalizes known results by J. Ginsburg and G. Saks, G. Saks, S. García-Ferreira, and others, for initial compactness. Departamento de Matemáticas, Universidad de los Andes Apartado Aéreo 4976, Bogotá, Colombia
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