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Theorems · Theorem · logic and foundations

FirstOrder.Field.ACF_isSatisfiable

∀ {p : ℕ}, Nat.Prime p ∨ p = 0 → (FirstOrder.Language.Theory.ACF p).IsSatisfiable
Defined in
Mathlib.ModelTheory.Algebra.Field.IsAlgClosed
Cited by
1 results in Mathlib
Foundations
Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Field.ACF_isComplete · cited by 3Field.ACF_isCompleteFact · cited by 2726FactNat.Prime · cited by 2059Nat.PrimeZMod · cited by 1024ZModAlgebraicClosure · cited by 53AlgebraicClosureFirstOrder.Language.ring · cited by 36Language.ringFirstOrder.Ring.CompatibleRing · cited by 27Ring.CompatibleRingFirstOrder.Language.Theory.IsSatisfiable · cited by 25Theory.IsSatisfiableFirstOrder.Language.Theory.ACF · cited by 11Theory.ACFFirstOrder.Ring.compatibleRingOfRing · cited by 3Ring.compatibleRingOfRingField.ACF_isSatisfiableCITED BYCITES

Cites9

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

Cited by1

Results whose statement or proof uses this declaration.