Theorems · Theorem · logic and foundations
FirstOrder.Language.Structure.cg_iff
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M],
FirstOrder.Language.Structure.CG L M ↔ ∃ S, S.Countable ∧ (FirstOrder.Language.Substructure.closure L).toFun S = ⊤An equivalent expression of Structure.cg.
- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 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
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.Countablestatement and proof · cited by 545
- FirstOrder.Language.Substructurestatement · cited by 242
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- FirstOrder.Language.Structure.CGstatement · cited by 16
- FirstOrder.Language.Structure.cg_defproof · cited by 6
- FirstOrder.Language.Substructure.cg_defproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.