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I'm not sure whether this is more "down-to-earth" but take 0-1 laws of random graphs. The probability of a first order property to be satisfied by a random graph distributed $G(n,p)$ tends to 0 or 1.
I'm not sure whether this is more "down-to-earth" but take 0-1 laws of random graphs. The probability of a first order property to be satisfied by a random graph distributed $G(n,p)$ tends to 0 or 1.