Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.FG
{L : FirstOrder.Language} → {M : Type u_1} → [inst : L.Structure M] → L.Substructure M → PropA substructure of M is finitely generated if it is the closure of a finite subset of M.
- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
Cited by40
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.fg_iff_structure_fgstatement and proof · cited by 12
- FirstOrder.Language.FGEquivproof · cited by 9
- FirstOrder.Language.Structure.FG.rangestatement and proof · cited by 7
- FirstOrder.Language.Substructure.fg_defstatement and proof · cited by 6
- FirstOrder.Language.Structure.fg_defstatement and proof · cited by 6
- FirstOrder.Language.IsUltrahomogeneousproof · cited by 5
- FirstOrder.Language.Substructure.FG.supstatement and proof · cited by 5
- FirstOrder.Language.Substructure.fg_closure_singletonstatement · cited by 4
- FirstOrder.Language.Substructure.fg_closurestatement · cited by 3
- FirstOrder.Language.Substructure.FG.cgstatement and proof · cited by 3
- FirstOrder.Language.Substructure.FG.finitestatement and proof · cited by 3
- FirstOrder.Language.age.countable_quotientproof · cited by 2