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I suggest that a classification for finite models is in practice equivalent to a polynomial-time algorithm for the number of models of size ''n''. There are some refinements and variations of this idea: for example if the number of models of size n is polynomial in n then one would presumably want a polynomial-time algorithm that lists them all. Something like permutations are obviously classifiable in any reasonable sens, but the number of types of size n grows more than polynomially fast in n, so one cant always demand a polynomial-time listing of them.