Theorems · Definition · logic and foundations
FirstOrder.Language.Substructure.CG
{L : FirstOrder.Language} → {M : Type u_1} → [inst : L.Structure M] → L.Substructure M → PropA substructure of M is countably generated if it is the closure of a countable subset of M.
- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 18 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.
- Setproof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Countableproof · cited by 545
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
Cited by20
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.cg_defstatement and proof · cited by 6
- FirstOrder.Language.Substructure.cg_defstatement and proof · cited by 5
- FirstOrder.Language.Substructure.FG.cgstatement · cited by 3
- FirstOrder.Language.Structure.CG.casesOnstatement and proof · cited by 2
- FirstOrder.Language.Structure.CG.outstatement · cited by 2
- FirstOrder.Language.equiv_between_cgproof · cited by 2
- FirstOrder.Language.Substructure.CG.mapstatement and proof · cited by 2
- FirstOrder.Language.Substructure.cg_iff_countablestatement and proof · cited by 1
- FirstOrder.Language.Structure.CG.map_of_surjectiveproof · cited by 1
- FirstOrder.Language.Structure.CG.rangestatement and proof · cited by 1
- FirstOrder.Language.Substructure.CG.of_map_embeddingstatement and proof · cited by 1
- FirstOrder.Language.Substructure.cg_botstatement · cited by 0