Positive results in abstract model theory: a theory of compact logics
(From the authors summary) 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. We also prove some combinatorial results of independent interest.
scientific article; zbMATH DE number 3865254
scientific article