Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.model_iff
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] (T : L.Theory), M ⊨ T ↔ ∀ φ ∈ T, M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 3 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.
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 and proof · cited by 127
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Sentence.Realizestatement and proof · cited by 62
- FirstOrder.Language.Theory.Model.realize_of_memproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentenceproof · cited by 5
- FirstOrder.Language.Theory.model_iff_subset_completeTheoryproof · cited by 2
- FirstOrder.Language.Theory.models_of_models_theoryproof · cited by 1