Positive results in abstract model theory: a theory of compact logics

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Annals of Pure and Applied Logic 25 (3):263-299 (1983)
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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. We also prove some combinatorial results of independent interest

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10.1016/0168-0072(83)90021-0

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Citations of this work

Remarks in abstract model theory.Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (3):255-288.
Limit ultrapowers and abstract logics.Paolo Lipparini - 1987 - Journal of Symbolic Logic 52 (2):437-454.

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References found in this work

Axioms for abstract model theory.K. Jon Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
Stationary logic.Jon Barwise - 1978 - Annals of Mathematical Logic 13 (2):171.
Axioms for abstract model theory.K. J. Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
On descendingly complete ultrafilters.Karel Prikry - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 459--488.
δ-Logics and generalized quantifiers.J. A. Makowsky - 1976 - Annals of Mathematical Logic 10 (2):155-192.

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