Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.cg_iff_countable
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] [Countable ((l : ℕ) × L.Functions l)]
{s : L.Substructure M}, s.CG ↔ Countable ↥s- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Countablestatement and proof · cited by 633
- Set.Countableproof · cited by 545
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.Functionsstatement and proof · cited by 153
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
- FirstOrder.Language.Substructure.CGstatement and proof · cited by 18
- FirstOrder.Language.Substructure.closure_eqproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.cg_iff_countableproof · cited by 1