Mathlib Map

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
Assumes
FirstOrder.Language.Structure

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.Hereditary · cited by 5Language.HereditaryFirstOrder.Language.IsFraisseLimit.age · cited by 3IsFraisseLimit.ageFirstOrder.Language.Embedding.age_subset_age · cited by 2Embedding.age_subset_ageFirstOrder.Language.age.countable_quotient · cited by 2age.countable_quotientFirstOrder.Language.age.hereditary · cited by 2age.hereditaryFirstOrder.Language.age.jointEmbedding · cited by 2age.jointEmbeddingFirstOrder.Language.age.nonempty · cited by 2age.nonemptyFirstOrder.Language.dlo_age · cited by 1Language.dlo_ageFirstOrder.Language.IsFraisseLimit.isExtensionPair · cited by 1IsFraisseLimit.isExtensio…FirstOrder.Language.exists_cg_is_age_of · cited by 1Language.exists_cg_is_age…FirstOrder.Language.Structure.FG.mem_age_of_equiv · cited by 1FG.mem_age_of_equivFirstOrder.Language.IsUltrahomogeneous.age_isFraisse · cited by 1IsUltrahomogeneous.age_is…FirstOrder.Language.IsUltrahomogeneous.amalgamation_age · cited by 1IsUltrahomogeneous.amalga…FirstOrder.Language.age_directLimit · cited by 1Language.age_directLimitFirstOrder.Language.age.is_equiv_invariant · cited by 1age.is_equiv_invariantSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureCategoryTheory.Bundled.α · cited by 736Bundled.αFirstOrder.Language.Embedding · cited by 128Language.EmbeddingCategoryTheory.Bundled · cited by 42CategoryTheory.BundledFirstOrder.Language.Structure.FG · cited by 27Structure.FGLanguage.ageCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.