Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.cg_def
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : L.Substructure M},
N.CG ↔ ∃ S, S.Countable ∧ (FirstOrder.Language.Substructure.closure L).toFun S = N- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Countablestatement · cited by 545
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunstatement · cited by 105
- FirstOrder.Language.Substructure.closurestatement · cited by 70
- FirstOrder.Language.Substructure.CGstatement and proof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.CG.mapproof · cited by 2
- FirstOrder.Language.Substructure.CG.of_map_embeddingproof · cited by 1
- FirstOrder.Language.Substructure.CG.supproof · cited by 0
- FirstOrder.Language.Structure.cg_iffproof · cited by 0