Annals of Pure and Applied Logic 25 (3):263-299 (1983)
| 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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| DOI | 10.1016/0168-0072(83)90021-0 |
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References found in this work BETA
Axioms for Abstract Model Theory.K. Jon 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.
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Citations of this work BETA
Remarks in Abstract Model Theory.Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (3):255-288.
Harmonious Logic: Craig’s Interpolation Theorem and its Descendants.Solomon Feferman - 2008 - Synthese 164 (3):341 - 357.
Harmonious Logic: Craig’s Interpolation Theorem and its Descendants.Solomon Feferman - 2008 - Synthese 164 (3):341-357.
The Craig Interpolation Theorem in Abstract Model Theory.Jouko Väänänen - 2008 - Synthese 164 (3):401-420.
Limit Ultrapowers and Abstract Logics.Paolo Lipparini - 1987 - Journal of Symbolic Logic 52 (2):437-454.
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