Theorems · Definition · logic and foundations
FirstOrder.Language.IsUltrahomogeneous
(L : FirstOrder.Language) → (M : Type w) → [L.Structure M] → Prop
A structure M is ultrahomogeneous if every embedding of a finitely generated substructure
into M extends to an automorphism of M.
- Defined in
- Mathlib.ModelTheory.Fraisse
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructureproof · cited by 242
- FirstOrder.Language.Embeddingproof · cited by 128
- FirstOrder.Language.Equivproof · cited by 83
- FirstOrder.Language.Substructure.subtypeproof · cited by 40
- FirstOrder.Language.Embedding.compproof · cited by 38
- FirstOrder.Language.Equiv.toEmbeddingproof · cited by 34
- FirstOrder.Language.Substructure.FGproof · cited by 34
Cited by7
Results whose statement or proof uses this declaration.
- FirstOrder.Language.IsFraisseLimit.ultrahomogeneousstatement · cited by 2
- FirstOrder.Language.IsUltrahomogeneous.extend_embeddingstatement and proof · cited by 2
- FirstOrder.Language.IsUltrahomogeneous.age_isFraissestatement and proof · cited by 1
- FirstOrder.Language.IsUltrahomogeneous.amalgamation_agestatement and proof · cited by 1
- FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPairstatement and proof · cited by 1
- FirstOrder.Language.IsFraisseLimit.recOnstatement and proof · cited by 0
- FirstOrder.Language.IsFraisseLimit.casesOnstatement and proof · cited by 0