Theorems · Definition · logic and foundations
FirstOrder.Language.IsExtensionPair
(L : FirstOrder.Language) → (M : Type w) → (N : Type w') → [L.Structure M] → [L.Structure N] → Prop
Two structures M and N form an extension pair if the domain of any finitely-generated map
from M to N can be extended to include any element of M.
- Defined in
- Mathlib.ModelTheory.PartialEquiv
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.PartialEquiv.domproof · cited by 35
- FirstOrder.Language.FGEquivproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- FirstOrder.Language.equiv_between_cgstatement and proof · cited by 2
- FirstOrder.Language.IsExtensionPair.definedAtLeftstatement and proof · cited by 2
- FirstOrder.Language.IsFraisseLimit.isExtensionPairstatement · cited by 1
- FirstOrder.Language.IsExtensionPair.definedAtRightstatement and proof · cited by 1
- FirstOrder.Language.isExtensionPair_iff_codstatement and proof · cited by 1
- FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_supstatement and proof · cited by 1
- FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPairstatement and proof · cited by 1
- FirstOrder.Language.dlo_isExtensionPairstatement · cited by 1
- FirstOrder.Language.IsExtensionPair.codstatement · cited by 0
- FirstOrder.Language.embedding_from_cgstatement and proof · cited by 0