Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.Theory.ModelType.of

{L : FirstOrder.Language} →
  (T : L.Theory) → (M : Type w) → [inst : L.Structure M] → [M ⊨ T] → [Nonempty M] → T.ModelType

The object in the category of R-algebras associated to a type equipped with the appropriate typeclasses.

Defined in
Mathlib.ModelTheory.Bundled
Cited by
5 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Theory.ModelNonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.Theory.Model.bundled · cited by 5Model.bundledFirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiable · cited by 3Theory.isSatisfiable_iff_…FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence · cited by 1Theory.models_formula_iff…FirstOrder.Language.Theory.simpleGraph_isSatisfiable · cited by 0Theory.simpleGraph_isSati…FirstOrder.Language.Theory.ModelType.coe_of · cited by 0ModelType.coe_ofFirstOrder.Language.dlo_isComplete · cited by 0Language.dlo_isCompleteFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeModelType.ofCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.