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Theorems · Definition · logic and foundations

FirstOrder.Language.ElementarilyEquivalent.toModel

{L : FirstOrder.Language} →
  (T : L.Theory) →
    {M : T.ModelType} → {N : Type u_1} → [LN : L.Structure N] → L.ElementarilyEquivalent (↑M) N → T.ModelType

A structure that is elementarily equivalent to a model, bundled as a model.

Defined in
Mathlib.ModelTheory.Bundled
Cited by
1 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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Cardinal.Categorical.isComplete · cited by 3Categorical.isCompleteFirstOrder.Language.ElementarySubstructure.toModel · cited by 1ElementarySubstructure.to…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelType.Carrier · cited by 59ModelType.CarrierFirstOrder.Language.ElementarilyEquivalent · cited by 19Language.ElementarilyEqui…ElementarilyEquivalent.toModelCITED BYCITES

Cites6

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Cited by2

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