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Theorems · Definition · logic and foundations

FirstOrder.Language.MeetsDefinable.toElementarySubstructure

{L : FirstOrder.Language} →
  {M : Type u_1} →
    [inst : L.Structure M] → {A : Set M} → FirstOrder.Language.MeetsDefinable A → L.ElementarySubstructure M

Bundles the closure of a set meeting definable sets as an elementary substructure.

Defined in
Mathlib.ModelTheory.ElementarySubstructures
Cited by
0 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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Set · cited by 53352SetFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunFirstOrder.Language.Substructure.closure · cited by 70Substructure.closureFirstOrder.Language.ElementarySubstructure · cited by 18Language.ElementarySubstr…FirstOrder.Language.MeetsDefinable · cited by 3Language.MeetsDefinableFirstOrder.Language.MeetsDefinable.isElementary_closure · cited by 0MeetsDefinable.isElementa…MeetsDefinable.toElementarySu…CITED BYCITES

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