Theorems · Definition · logic and foundations
FirstOrder.Field.fieldOfModelACF
(p : ℕ) → (K : Type u_2) → [inst : FirstOrder.Language.ring.Structure K] → [h : K ⊨ FirstOrder.Language.Theory.ACF p] → Field K
A model for the Theory of algebraically closed fields is a Field. After introducing
this as a local instance on a particular Type, you should usually also introduce
modelField_of_modelACF p M, compatibleRingOfModelField and isAlgClosed_of_model_ACF
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement · cited by 7,404
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.ringstatement and proof · cited by 36
- FirstOrder.Language.Theory.ACFstatement and proof · cited by 11
- FirstOrder.Language.Theory.fieldproof · cited by 6
- FirstOrder.Field.modelField_of_modelACFproof · cited by 3
- FirstOrder.Field.fieldOfModelFieldproof · cited by 0
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Field.ACF_isCompleteproof · cited by 3
- FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realizeproof · cited by 2
- FirstOrder.Field.ACF_categoricalproof · cited by 1