Theorems · Definition · logic and foundations
FirstOrder.Language.elementaryDiagram
(L : FirstOrder.Language) → (M : Type u_1) → [L.Structure M] → (L.withConstants M).Theory
The elementary diagram of an L-structure is the set of all sentences with parameters it
satisfies.
- Defined in
- Mathlib.ModelTheory.ElementaryMaps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Theorystatement · cited by 154
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.completeTheoryproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagramstatement and proof · cited by 2
- FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_geproof · cited by 1
- FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram_toFunstatement and proof · cited by 0