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Theorems · Inductive type · logic and foundations

FirstOrder.Language.ElementarySubstructure

(L : FirstOrder.Language) → (M : Type u_1) → [L.Structure M] → Type u_1

An elementary substructure is one in which every formula applied to a tuple in the substructure agrees with its value in the overall structure.

Defined in
Mathlib.ModelTheory.ElementarySubstructures
Cited by
18 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language.ElementarySubstructure.subtype · cited by 7ElementarySubstructure.su…FirstOrder.Language.Substructure.elementarySkolem₁Reduct · cited by 4Substructure.elementarySk…FirstOrder.Language.ElementarySubstructure.toSubstructure · cited by 3ElementarySubstructure.to…FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_le · cited by 2Language.exists_elementar…FirstOrder.Language.Substructure.toElementarySubstructure · cited by 1Substructure.toElementary…FirstOrder.Language.Substructure.coeSort_elementarySkolem₁Reduct · cited by 1Substructure.coeSort_elem…FirstOrder.Language.ElementarySubstructure.isElementary' · cited by 1ElementarySubstructure.is…FirstOrder.Language.ElementarySubstructure.toModel · cited by 1ElementarySubstructure.to…FirstOrder.Language.ElementarySubstructure.mk.inj · cited by 1mk.injFirstOrder.Language.ElementarySubstructure.mk.noConfusion · cited by 1mk.noConfusionFirstOrder.Language.exists_elementarySubstructure_card_eq · cited by 1Language.exists_elementar…FirstOrder.Language.ElementarySubstructure.casesOn · cited by 0ElementarySubstructure.ca…FirstOrder.Language.ElementarySubstructure.coe_subtype · cited by 0ElementarySubstructure.co…FirstOrder.Language.ElementarySubstructure.coe_top · cited by 0ElementarySubstructure.co…FirstOrder.Language.ElementarySubstructure.ctorIdx · cited by 0ElementarySubstructure.ct…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureLanguage.ElementarySubstructu…CITED BYCITES

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