Theorems · Theorem · logic and foundations
FirstOrder.Language.age.nonempty
∀ {L : FirstOrder.Language} (M : Type w) [inst : L.Structure M], (L.age M).Nonempty- Defined in
- Mathlib.ModelTheory.Fraisse
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 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.
- Set.Nonemptystatement · cited by 2,627
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
- CategoryTheory.Bundledstatement · cited by 42
- FirstOrder.Language.Substructure.subtypeproof · cited by 40
- Set.finite_emptyproof · cited by 26
- FirstOrder.Language.agestatement · cited by 18
- FirstOrder.Language.Substructure.fg_iff_structure_fgproof · cited by 12
- CategoryTheory.Bundled.ofproof · cited by 6
- FirstOrder.Language.Substructure.fg_closureproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.IsUltrahomogeneous.age_isFraisseproof · cited by 1
- FirstOrder.Language.exists_countable_is_age_of_iffproof · cited by 0