Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.fg_def
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : L.Substructure M},
N.FG ↔ ∃ S, S.Finite ∧ (FirstOrder.Language.Substructure.closure L).toFun S = N- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetproof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Finitestatement and proof · cited by 1,814
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- Finset.finite_toSetproof · cited by 210
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- FirstOrder.Language.Substructure.FGstatement and proof · cited by 34
- Set.Finite.exists_finset_coeproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.FG.supproof · cited by 5
- FirstOrder.Language.Substructure.FG.cgproof · cited by 3
- FirstOrder.Language.Substructure.FG.mapproof · cited by 2
- FirstOrder.Language.Structure.fg_iffproof · cited by 1
- FirstOrder.Language.Substructure.FG.of_map_embeddingproof · cited by 1
- FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_familyproof · cited by 0