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Theorems · Theorem · logic and foundations

Set.definable_iff_empty_definable_with_params

∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {s : Set (α → M)},
  A.Definable L s ↔ ∅.Definable (L.withConstants ↑A) s
Defined in
Mathlib.ModelTheory.Definability
Cited by
1 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
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Set.Definable.mono · cited by 4Definable.monoSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.withConstants · cited by 108Language.withConstantsSet.Definable · cited by 39Set.DefinableSet.empty_definable_iff · cited by 2Set.empty_definable_iffSet.definable_iff_empty_defin…CITED BYCITES

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