Theorems · Theorem · logic and foundations
FirstOrder.Language.Structure.cg_iff_countable
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] [Countable ((l : ℕ) × L.Functions l)],
FirstOrder.Language.Structure.CG L M ↔ Countable M- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Countablestatement and proof · cited by 633
- FirstOrder.Language.Functionsstatement and proof · cited by 153
- FirstOrder.Language.Structure.CGstatement · cited by 16
- FirstOrder.Language.Equiv.toEquivproof · cited by 12
- FirstOrder.Language.Structure.cg_defproof · cited by 6
- FirstOrder.Language.Substructure.topEquivproof · cited by 4
- Equiv.countable_iffproof · cited by 2
- FirstOrder.Language.Substructure.cg_iff_countableproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.exists_countable_is_age_of_iffproof · cited by 0