Concerning the finite model property for propositional calculi
John Anderson · Proceedings of the American Mathematical Society · 1968
Introduction. For the definitions of propositional calculi, models and the finite model property (f.m.p.) we refer to [I] (we use 'model' for 'strong model'). In this note we describe two equivalent propositional calculi (equivalent in that they have identical sets of theorems) which differ in that one has the f.m.p. and the other does not, and in fact has no nontrivial finite model at all. This shows the f.m.p. is an attribute of a propositional calculus and not of the equivalence class of the calculus, unlike, for instance, decidability. I should like to thank R. Harrop for conversations on the topics of this paper, and also thank the referee for suggesting considerable improvements.