Theorems · Theorem · logic and foundations
Set.definable_iff_finitely_definable
∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {s : Set (α → M)},
A.Definable L s ↔ ∃ A0, ↑A0 ⊆ A ∧ (↑A0).Definable L s- Defined in
- Mathlib.ModelTheory.Definability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.extproof · cited by 2,266
- FirstOrder.Languagestatement and proof · cited by 1,084
- Finset.imageproof · cited by 910
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Finset.coe_imageproof · cited by 222
- Subtype.coe_etaproof · cited by 110
- FirstOrder.Language.Formulaproof · cited by 93
Cited by1
Results whose statement or proof uses this declaration.
- ax_grothendieck_of_definableproof · cited by 1