With respect to a modal logic , a property satisfied by when for any formula in the language of , if there is a Kripke model with a possible world at which is true, then there exists a finite Kripke model (i.e., whose set of possible worlds is finite) with a world at which is true. When is a sound and complete modal logic that extends classical logic, this condition may be equivalently stated as the property that if (i.e., is not an -theorem), there exists a finite Kripke model with a possible world at which is true. That a modal logic has the finite model property is frequently an important ingredient in proving it to be decidable.