Theorems · Inductive type · logic and foundations
FirstOrder.Language.Equiv
(L : FirstOrder.Language) → (M : Type w) → (N : Type w') → [L.Structure M] → [L.Structure N] → Type (max w w')
An equivalence of first-order structures is an equivalence that commutes with the interpretations of functions and relations.
- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.Structurestatement · cited by 775
Cited by114
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Equiv.toEmbeddingstatement · cited by 34
- FirstOrder.Language.Equiv.symmstatement and proof · cited by 32
- FirstOrder.Language.PartialEquiv.toEquivstatement · cited by 24
- FirstOrder.Language.Embedding.equivRangestatement · cited by 14
- FirstOrder.Language.Equiv.compstatement and proof · cited by 12
- FirstOrder.Language.Equiv.toEquivstatement and proof · cited by 12
- FirstOrder.Language.Equiv.toHomstatement · cited by 11
- FirstOrder.Language.Equiv.reflstatement · cited by 7
- FirstOrder.Language.Equiv.apply_symm_applystatement and proof · cited by 6
- FirstOrder.Language.IsUltrahomogeneousproof · cited by 5
- FirstOrder.Language.PartialEquiv.casesOnstatement and proof · cited by 5
- FirstOrder.Language.Equiv.extstatement and proof · cited by 4