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Theorems · Inductive type · logic and foundations

FirstOrder.Language.Structure.CG

(L : FirstOrder.Language) → (M : Type u_1) → [L.Structure M] → Prop

A structure is countably generated if it is the closure of a countable subset.

Defined in
Mathlib.ModelTheory.FinitelyGenerated
Cited by
16 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
FirstOrder.Language.Structure
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Around this declaration

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FirstOrder.Language.Structure.cg_def · cited by 6Structure.cg_defFirstOrder.Language.Structure.CG.casesOn · cited by 2CG.casesOnFirstOrder.Language.Structure.CG.out · cited by 2CG.outFirstOrder.Language.equiv_between_cg · cited by 2Language.equiv_between_cgFirstOrder.Language.Structure.cg_of_countable · cited by 2Structure.cg_of_countableFirstOrder.Language.DirectLimit.cg · cited by 1DirectLimit.cgFirstOrder.Language.Structure.CG.map_of_surjective · cited by 1CG.map_of_surjectiveFirstOrder.Language.Structure.CG.range · cited by 1CG.rangeFirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPair · cited by 1Language.isUltrahomogeneo…FirstOrder.Language.Structure.FG.cg · cited by 1FG.cgFirstOrder.Language.exists_cg_is_age_of · cited by 1Language.exists_cg_is_age…FirstOrder.Language.Structure.cg_iff_countable · cited by 1Structure.cg_iff_countableFirstOrder.Language.Substructure.cg_iff_structure_cg · cited by 0Substructure.cg_iff_struc…FirstOrder.Language.Structure.CG.recOn · cited by 0CG.recOnFirstOrder.Language.embedding_from_cg · cited by 0Language.embedding_from_cgFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureStructure.CGCITED BYCITES

Cites2

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Cited by18

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