منابع مشابه
Shelah’s Singular Compactness Theorem
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The best-known version of Shelah’s celebrated singular cardinal compactness theorem states that if the cardinality of an abelian group is singular, and all its subgroups of lesser cardinality are free, then the group itself is free. The proof can be adapted to cover a number of analogous situations in the setting of non-abelian groups, modules, graph colorings, set transversals etc. We give a s...
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In this talk we investigate the compactness theorem (as a property) in non-classical logics. We focus on the following problems: (a) What kind of semantics make a logic having compactnesss theorem? (b) What is the relationship between the compactness theorem and the classical model existence theorem (CME)/model existence theorem?
متن کاملThe Abstract Compactness Theorem revisited
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 correspo...
متن کاملThe Kolmogorov–riesz Compactness Theorem
We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly’s theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2008
ISSN: 0214-1493
DOI: 10.5565/publmat_52108_01