On the Axiomatization of Finite K-Frames

We find a short way to construct a formula which axiomatizes a given finite frame of the modal logic K, in the sense that for each finite frame A, we construct a formula ωA which holds in those and only those frames in which every formula true in A holds. To obtain this result we find, for each finite model {Mathematical expression} and each natural number n, a formula ω {Mathematical expression} which holds in those and only those models in which every formula true in {Mathematical expression}, and involving the first n propositional letters, holds. © 1983 Polish Academy of Sciences.