Theorems · Theorem · logic and foundations
FirstOrder.Language.Structure.fg_iff
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M],
FirstOrder.Language.Structure.FG L M ↔ ∃ S, S.Finite ∧ (FirstOrder.Language.Substructure.closure L).toFun S = ⊤An equivalent expression of Structure.FG in terms of Set.Finite instead of Finset.
- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 1 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
- 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 · cited by 242
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- FirstOrder.Language.Structure.FGstatement · cited by 27
- FirstOrder.Language.Substructure.fg_defproof · cited by 6
- FirstOrder.Language.Structure.fg_defproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.FG.countable_homproof · cited by 0