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Theorems · Definition · logic and foundations

FirstOrder.Language.ElementarySubstructure.subtype

{L : FirstOrder.Language} →
  {M : Type u_1} → [inst : L.Structure M] → (S : L.ElementarySubstructure M) → L.ElementaryEmbedding (↥S) M

The natural embedding of an L.Substructure of M into M.

Defined in
Mathlib.ModelTheory.ElementarySubstructures
Cited by
7 results in Mathlib
Foundations
Depth 30 from the axioms · uses Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

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FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_le · cited by 2Language.exists_elementar…FirstOrder.Language.ElementarySubstructure.meetsDefinable · cited by 0ElementarySubstructure.me…FirstOrder.Language.ElementarySubstructure.coe_subtype · cited by 0ElementarySubstructure.co…FirstOrder.Language.ElementarySubstructure.realize_sentence · cited by 0ElementarySubstructure.re…FirstOrder.Language.ElementarySubstructure.elementarilyEquivalent · cited by 0ElementarySubstructure.el…FirstOrder.Language.ElementarySubstructure.subtype_apply · cited by 0ElementarySubstructure.su…FirstOrder.Language.ElementarySubstructure.subtype_injective · cited by 0ElementarySubstructure.su…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.ElementaryEmbedding · cited by 33Language.ElementaryEmbedd…FirstOrder.Language.ElementarySubstructure · cited by 18Language.ElementarySubstr…FirstOrder.Language.ElementarySubstructure.isElementary · cited by 0ElementarySubstructure.is…ElementarySubstructure.subtypeCITED BYCITES

Cites5

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Cited by7

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