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Finite Partitions and Their Generators

Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (13-18):255-260 (1974)

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Classifying?0-categorical theories.George Weaver - 1988 - Studia Logica 47 (4):327-345.details Among the complete ℵ0-categorical theories with finite non-logical vocabularies, we distinguish three classes. The classification is obtained by looking at the number of bound variables needed to isolated complete types. In classI theories, all types are isolated by quantifier free formulas; in classII theories, there is a leastm, greater than zero, s.t. all types are isolated by formulas in no more thanm bound variables: and in classIII theories, for eachm there is a type which cannot be isolated inm or fewer (...) Download Export citation Bookmark 1 citation
From finitary to infinitary second‐order logic.George Weaver & Irena Penev - 2005 - Mathematical Logic Quarterly 51 (5):499-506.details A back and forth condition on interpretations for those second-order languages without functional variables whose non-logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second-order languages with an infinite non-logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second-order languages whose non-logical (...) Download Export citation Bookmark 2 citations

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