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Well then consider the sentence $\forall x(P(x)\vee\neg P(x))$. This has a model of size 2 but no model of size 3 in your sense. Because of the three elements, two have to agree about whether they satisfy $P$ and so there is nothing left to distinguish them.
@Joel: I suppose we are not looking at finite observation data, but rather observing what has transpired at time $\omega$ (infinity). @Robin: It should be non-zero because there is at least one DFA.
@Jacques: one could say that the size of a number in (0,1) is inessential, whereas asymptotic properties of the sequence of binary digits in the number are essential. Chaitin's Omega can also be anywhere in (0,1), but it is always a Martin-Löf random number.
