Theorems · Definition · logic and foundations
FirstOrder.Language.age
(L : FirstOrder.Language) → (M : Type w) → [L.Structure M] → Set (CategoryTheory.Bundled L.Structure)
The age of a structure M is the class of finitely-generated structures that embed into it.
- Defined in
- Mathlib.ModelTheory.Fraisse
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- CategoryTheory.Bundled.αproof · cited by 736
- FirstOrder.Language.Embeddingproof · cited by 128
- CategoryTheory.Bundledstatement and proof · cited by 42
- FirstOrder.Language.Structure.FGproof · cited by 27
Cited by21
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Hereditaryproof · cited by 5
- FirstOrder.Language.IsFraisseLimit.agestatement · cited by 3
- FirstOrder.Language.Embedding.age_subset_agestatement · cited by 2
- FirstOrder.Language.age.countable_quotientstatement and proof · cited by 2
- FirstOrder.Language.age.hereditarystatement and proof · cited by 2
- FirstOrder.Language.age.jointEmbeddingstatement and proof · cited by 2
- FirstOrder.Language.age.nonemptystatement · cited by 2
- FirstOrder.Language.dlo_agestatement · cited by 1
- FirstOrder.Language.IsFraisseLimit.isExtensionPairproof · cited by 1
- FirstOrder.Language.exists_cg_is_age_ofstatement and proof · cited by 1
- FirstOrder.Language.Structure.FG.mem_age_of_equivstatement · cited by 1
- FirstOrder.Language.IsUltrahomogeneous.age_isFraissestatement and proof · cited by 1