Theorems · Definition · logic and foundations
FirstOrder.Language.Hereditary
{L : FirstOrder.Language} → Set (CategoryTheory.Bundled L.Structure) → PropA class K has the hereditary property when all finitely-generated structures that embed into
structures in K are also in K.
- Defined in
- Mathlib.ModelTheory.Fraisse
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- CategoryTheory.Bundled.αproof · cited by 736
- CategoryTheory.Bundledstatement and proof · cited by 42
- FirstOrder.Language.ageproof · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Hereditary.is_equiv_invariant_of_fgstatement and proof · cited by 2
- FirstOrder.Language.age.hereditarystatement · cited by 2
- FirstOrder.Language.exists_cg_is_age_ofstatement and proof · cited by 1
- FirstOrder.Language.IsFraisse.hereditarystatement · cited by 1
- FirstOrder.Language.exists_countable_is_age_of_iffstatement and proof · cited by 0
- FirstOrder.Language.IsFraisse.casesOnstatement and proof · cited by 0
- FirstOrder.Language.IsFraisse.recOnstatement and proof · cited by 0