Theorems · Theorem · logic and foundations
FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPair
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M],
FirstOrder.Language.Structure.CG L M → (L.IsUltrahomogeneous M ↔ L.IsExtensionPair M M)A countably generated structure is ultrahomogeneous if and only if any equivalence between finitely generated substructures can be extended to any element in the domain.
- Defined in
- Mathlib.ModelTheory.Fraisse
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- LE.le.transproof · cited by 3,151
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- FirstOrder.Language.Substructureproof · cited by 242
- Set.mem_singletonproof · cited by 183
- Set.inclusionproof · cited by 145
- FirstOrder.Language.Embeddingproof · cited by 128
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Equivproof · cited by 83
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.isFraisseLimit_of_countable_nonempty_dloproof · cited by 2