Theorems · Definition · logic and foundations
FirstOrder.Language.Theory.ModelType.reduct
{L : FirstOrder.Language} →
{T : L.Theory} → {L' : FirstOrder.Language} → (φ : L →ᴸ L') → (φ.onTheory T).ModelType → T.ModelTypeThe reduct of any model of φ.onTheory T is a model of T.
- Defined in
- Mathlib.ModelTheory.Bundled
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, 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.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.LHomstatement and proof · cited by 66
- FirstOrder.Language.Theory.ModelTypestatement and proof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.LHom.onTheorystatement and proof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheoryproof · cited by 1
- FirstOrder.Language.Theory.ModelType.reduct_Carrierstatement and proof · cited by 1
- FirstOrder.Language.Theory.exists_large_model_of_infinite_modelproof · cited by 1
- FirstOrder.Language.Theory.ModelType.reduct_strucstatement and proof · cited by 0
- FirstOrder.Language.Theory.exists_modelType_is_realized_inproof · cited by 0