Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.constantMap

{L : FirstOrder.Language} → {M : Type w} → [L.Structure M] → L.Constants → M

Interpretation of a constant symbol

Defined in
Mathlib.ModelTheory.Basic
Cited by
28 results in Mathlib
Foundations
Depth 10 from the axioms · uses Quot.sound
Assumes
FirstOrder.Language.Structure

Around this declaration

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

FirstOrder.Language.Term.realize_constants · cited by 6Term.realize_constantsFirstOrder.Language.HomClass.map_constants · cited by 4HomClass.map_constantsFirstOrder.Language.Formula.realize_equivSentence_symm_con · cited by 4Formula.realize_equivSent…FirstOrder.Language.Term.realize_varsToConstants · cited by 3Term.realize_varsToConsta…FirstOrder.Language.model_distinctConstantsTheory · cited by 2Language.model_distinctCo…FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram · cited by 2ElementaryEmbedding.ofMod…FirstOrder.Language.funMap_eq_coe_constants · cited by 2Language.funMap_eq_coe_co…FirstOrder.Language.Formula.realize_equivSentence · cited by 2Formula.realize_equivSent…FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_card_le · cited by 1Theory.isSatisfiable_unio…FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence · cited by 1Theory.models_formula_iff…FirstOrder.Language.Substructure.constants_mem · cited by 1Substructure.constants_memFirstOrder.Language.presburger.term_realize_eq_add_dotProduct · cited by 1presburger.term_realize_e…FirstOrder.Language.card_le_of_model_distinctConstantsTheory · cited by 1Language.card_le_of_model…Set.TermDefinable.const · cited by 1TermDefinable.constFirstOrder.Language.Term.realize_constantsToVars · cited by 1Term.realize_constantsToV…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Structure.funMap · cited by 69Structure.funMapFirstOrder.Language.Constants · cited by 14Language.ConstantsLanguage.constantMapCITED BYCITES

Cites4

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Cited by29

Results whose statement or proof uses this declaration.