Theorems · Theorem · logic and foundations

FirstOrder.Ring.mvPolynomial_zeroLocus_definable

∀ {ι : Type u_1} {K : Type u_2} [inst : Field K] [inst_1 : FirstOrder.Ring.CompatibleRing K]
  (S : Finset (MvPolynomial ι K)),
  (⋃ p ∈ S, (fun m => MvPolynomial.coeff m p) '' ↑p.support).Definable FirstOrder.Language.ring
    (MvPolynomial.zeroLocus K (Ideal.span ↑S))

Defined in: Mathlib.ModelTheory.Algebra.Ring.Definability
Cited by: 1 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field FirstOrder.Ring.CompatibleRing

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Cites40

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Finsetstatement and proof · cited by 13,712
SetLike.coestatement and proof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
Set.imagestatement and proof · cited by 5,609
Finsuppstatement and proof · cited by 5,255
Set.iUnionstatement and proof · cited by 2,483
MvPolynomialstatement and proof · cited by 2,140
Ideal.spanstatement · cited by 948

Cited by1

Results whose statement or proof uses this declaration.

ax_grothendieck_zeroLocusproof · cited by 1