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Theorems · Theorem · logic and foundations

Set.empty_definableFun_iff

∀ {M : Type u_1} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u_2} {f : (α → M) → M},
  Set.DefinableFun L ∅ f ↔ ∃ φ, Function.tupleGraph f = Set.ofPred φ.Realize
Defined in
Mathlib.ModelTheory.Definability
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language.Term.definableFun_realize · cited by 3Term.definableFun_realizeSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeSet.DefinableFun · cited by 15Set.DefinableFunFunction.tupleGraph · cited by 4Function.tupleGraphSet.empty_definableFun_iffCITED BYCITES

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