Then $F_n(x,y)$ converges to $F(x,y)$ uniformly in $x$.

One must also be aware that the curvature of $M_i$ might not be bounded uniformly in $i$.

Hence, although the topology of reducts of $A$ is uniformly controlled, so to speak, by that of $A$, the model theory of the reducts can be much wilder.

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