It was recently shown that the theories of generic algebraic curves converge to a limit theory as their degrees go to innity. In this paper we give quantitative versions of this result and other similar results. In particular, we show that generic curves of degree higher than 2 2r cannot be distinguished by a rst-order formula of quantier rank r. A decision algorithm for the limit theory then follows easily. We also show that in this theory all formulas are equivalent to boolean combinations of existential formulas, and give a quantitative version of this result
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