The limit theory of generic polynomials

Abstract : We show that the set T of first-order sentences satisfied by all generic polynomials of sufficiently high degree forms a complete theory. As a consequence, complex polynomials of even degree cannot be distinguished from complex polynomials of odd degree by a first-order formula. We ask whether T has an analytic model.
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Pascal Koiran. The limit theory of generic polynomials. [Research Report] LIP RR-2001-35, Laboratoire de l'informatique du parallélisme. 2001, 2+14p. ⟨hal-02102064⟩

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