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Back-and-forth systems for generic curves and a decision algorithm for the limit theory

✍ Scribed by Pascal Koiran; Natacha Portier

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
193 KB
Volume
111
Category
Article
ISSN
0168-0072

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✦ Synopsis

It was recently shown that the theories of generic algebraic curves converge to a limit theory as their degrees go to inΓΏnity. 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 ΓΏrst-order formula of quantiΓΏer 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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