Finite model property

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In logic, we say a logic L has the finite model property (fmp for short) if there is a class of models M of L (i.e. 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 the fmp, then it is decidable.

[edit] References

Blackburn P., de Rijke M., Venema Y. Modal Logic. Cambridge University Press, 2001.