Technical Report CS0254

Title: Positive Results in Abstract Model Theory: A Theory of Compact Logics
Authors: J. A. Makowsky and S. Shelah
Abstract: We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences.
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