Theorems · Inductive type · logic and foundations
FirstOrder.Language.Theory.Model
{L : FirstOrder.Language} → (M : Type w) → [L.Structure M] → L.Theory → PropA model of a theory is a structure in which every sentence is realized as true.
- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.Structurestatement · cited by 775
- FirstOrder.Language.Theorystatement · cited by 154
Cited by86
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.realize_sentence_of_memstatement and proof · cited by 11
- FirstOrder.Language.Theory.Model.bundledstatement and proof · cited by 5
- FirstOrder.Language.Theory.Model.isSatisfiablestatement and proof · cited by 5
- FirstOrder.Language.Theory.Model.monostatement and proof · cited by 5
- FirstOrder.Language.Theory.ModelType.ofstatement and proof · cited by 5
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentencestatement and proof · cited by 5
- FirstOrder.Language.Theory.Iff.realize_bd_iffstatement and proof · cited by 5
- FirstOrder.Language.Theory.ModelType.casesOnstatement and proof · cited by 4
- FirstOrder.Language.Theory.Model.realize_of_memstatement and proof · cited by 3
- FirstOrder.Language.simpleGraphOfStructurestatement and proof · cited by 3
- FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiableproof · cited by 3
- FirstOrder.Language.Theory.model_iffstatement and proof · cited by 3