Definable Subsets in the language of rings #
This file proves that the set of zeros of a multivariable polynomial is a definable subset.
theorem
FirstOrder.Ring.mvPolynomial_zeroLocus_definable
{ι : Type u_1}
{K : Type u_2}
[Field K]
[CompatibleRing K]
(S : Finset (MvPolynomial ι K))
:
(⋃ p ∈ S, ⇑p.coeff '' ↑p.support).Definable Language.ring (MvPolynomial.zeroLocus K (Ideal.span ↑S))