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Theorems · Theorem · logic and foundations

Set.termDefinable_empty_iff

∀ {M : Type w} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {f : (α → M) → M},
  ∅.TermDefinable L f ↔ ∃ φ, f = fun v => FirstOrder.Language.Term.realize v φ
Defined in
Mathlib.ModelTheory.Definability
Cited by
1 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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Set.termDefinable_empty_withConstants_iff · cited by 1Set.termDefinable_empty_w…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Term.realize · cited by 81Term.realizeEquiv.exists_congr_left · cited by 33Equiv.exists_congr_leftFirstOrder.Language.constantsOn · cited by 22Language.constantsOnFirstOrder.Language.LHom.id · cited by 18LHom.idSet.TermDefinable · cited by 12Set.TermDefinableFirstOrder.Language.LHom.onTerm · cited by 11LHom.onTermFirstOrder.Language.LHom.sumElim · cited by 9LHom.sumElimFirstOrder.Language.LHom.ofIsEmpty · cited by 6LHom.ofIsEmptyFirstOrder.Language.LEquiv.addEmptyConstants · cited by 5LEquiv.addEmptyConstantsSet.termDefinable_empty_iffCITED BYCITES

Cites19

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Cited by1

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