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Theorems · Theorem · logic and foundations

FirstOrder.Field.isAlgClosed_of_model_ACF

∀ (p : ℕ) (K : Type u_2) [inst : Field K] [inst_1 : FirstOrder.Ring.CompatibleRing K]
  [h : K ⊨ FirstOrder.Language.Theory.ACF p], IsAlgClosed K
Defined in
Mathlib.ModelTheory.Algebra.Field.IsAlgClosed
Cited by
2 results in Mathlib
Foundations
Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFirstOrder.Ring.CompatibleRingFirstOrder.Language.Theory.Model
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FirstOrder.Field.ACF_isComplete · cited by 3Field.ACF_isCompleteFirstOrder.Field.ACF_categorical · cited by 1Field.ACF_categoricalField · cited by 7404FieldSet.ofPred · cited by 6101Set.ofPredPolynomial · cited by 5681PolynomialSet.image · cited by 5609Set.imagePolynomial.natDegree · cited by 1105Polynomial.natDegreeIrreducible · cited by 496IrreduciblePolynomial.Monic · cited by 461Polynomial.MonicIsAlgClosed · cited by 150IsAlgClosedFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.ring · cited by 36Language.ringFirstOrder.Ring.CompatibleRing · cited by 27Ring.CompatibleRingPolynomial.natDegree_pos_iff_degree_pos · cited by 22Polynomial.natDegree_pos_…FirstOrder.Language.Theory.ACF · cited by 11Theory.ACFField.isAlgClosed_of_model_ACFCITED BYCITES

Cites20

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Cited by2

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