Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.model_iff_subset_completeTheory
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {T : L.Theory}, M ⊨ T ↔ T ⊆ L.completeTheory M- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 2 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.
Cites7
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 and proof · cited by 154
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.Theory.Modelstatement · cited by 67
- FirstOrder.Language.completeTheorystatement · cited by 14
- FirstOrder.Language.Theory.model_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementarilyEquivalent.theory_model_iffproof · cited by 3
- FirstOrder.Language.Theory.completeTheory.subsetproof · cited by 1