Theorems · Definition · logic and foundations
FirstOrder.Field.fieldOfModelField
(K : Type u_2) → [inst : FirstOrder.Language.ring.Structure K] → [K ⊨ FirstOrder.Language.Theory.field] → Field K
A model for the theory of fields is a field. To introduced locally on Types that don't
already have instances for ring operations.
When this is used, it is almost always useful to also add locally the instance
compatibleFieldOfModelField afterwards.
- Defined in
- Mathlib.ModelTheory.Algebra.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.fieldstatement and proof · cited by 6
- Field.ofMinimalAxiomsproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Field.compatibleRingOfModelFieldstatement · cited by 3
- FirstOrder.Field.fieldOfModelACFproof · cited by 3