Before revision: each model M is a model of L) such that any non-theorem of L is falsified by some finite model in M. Another way of putting this is to say that L has the fmp if for every formula A of L, A is an L-theorem iff A is a theorem of the theory of finite models of L. If L is finitely axiomatizable (and has a recursive set of recursive rules) and has the fmp, then it is decidable.
After revision: ineach model M is a model of L) such that any non-theorem of L is falsified by some finite model in M. Another way of putting this is to say that L has the fmp if for every formula A of L, A is an L-theorem iff A is a theorem of the theory of finite models of L. If L is finitely axiomatizable (and has a recursive set of recursive rules) and has the fmp, then it is decidable.