Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.fg_iff_structure_fg

∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] (S : L.Substructure M),
  S.FG ↔ FirstOrder.Language.Structure.FG L ↥S
Defined in
Mathlib.ModelTheory.FinitelyGenerated
Cited by
12 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.age.countable_quotient · cited by 2age.countable_quotientFirstOrder.Language.age.jointEmbedding · cited by 2age.jointEmbeddingFirstOrder.Language.age.nonempty · cited by 2age.nonemptyFirstOrder.Language.IsFraisseLimit.nonempty_equiv · cited by 1IsFraisseLimit.nonempty_e…FirstOrder.Language.IsUltrahomogeneous.amalgamation_age · cited by 1IsUltrahomogeneous.amalga…FirstOrder.Language.empty.isFraisseLimit_of_countable_infinite · cited by 1empty.isFraisseLimit_of_c…FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPair · cited by 1Language.isUltrahomogeneo…FirstOrder.Language.dlo_isExtensionPair · cited by 1Language.dlo_isExtensionP…FirstOrder.Language.IsFraisseLimit.isExtensionPair · cited by 1IsFraisseLimit.isExtensio…FirstOrder.Language.countable_self_fgequiv_of_countable · cited by 0Language.countable_self_f…FirstOrder.Language.age.fg_substructure · cited by 0age.fg_substructureFirstOrder.Language.PartialEquiv.dom_fg_iff_cod_fg · cited by 0PartialEquiv.dom_fg_iff_c…Top.top · cited by 9680Top.topFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Substructure.map · cited by 49Substructure.mapFirstOrder.Language.Embedding.toHom · cited by 40Embedding.toHomFirstOrder.Language.Substructure.subtype · cited by 40Substructure.subtypeFirstOrder.Language.Substructure.FG · cited by 34Substructure.FGFirstOrder.Language.Structure.FG · cited by 27Structure.FGFirstOrder.Language.Hom.range_eq_map · cited by 7Hom.range_eq_mapFirstOrder.Language.Structure.fg_def · cited by 6Structure.fg_defFirstOrder.Language.Substructure.range_subtype · cited by 3Substructure.range_subtypeFirstOrder.Language.Substructure.FG.map · cited by 2FG.mapFirstOrder.Language.Substructure.FG.of_map_embedding · cited by 1FG.of_map_embeddingSubstructure.fg_iff_structure…CITED BYCITES

Cites14

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

Cited by12

Results whose statement or proof uses this declaration.