Theorems · Theorem · logic and foundations
FirstOrder.Language.ElementarilyEquivalent.completeTheory_eq
∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N],
L.ElementarilyEquivalent M N → L.completeTheory M = L.completeTheory N- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 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.ElementarilyEquivalentstatement and proof · cited by 19
- FirstOrder.Language.completeTheorystatement · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementarilyEquivalent.theory_model_iffproof · cited by 3