Some compactness results for modal logic
A modal logic L is compact iff every L-consistent set of wff can be simultaneously satisfied at some point in a frame for L. L is canonical iff every theorem of L is valid on the frame of the canonical model of L. It is trivial that if L is canonical then L is compact. It is not known whether the converse holds. The author proves that the converse does hold for any logics whose frames contain no worlds with infinitely many alternatives. He then widens one of the classes of logics for which non- compactness is known, and another class of logics for which canonicity, and therefore compactness is known. He finally uses results obtained elsewhere to show that there are uncountably many canonical logics and uncountably many non compact extensions of S4 with the finite model property.
scientific article; zbMATH DE number 4116500