Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.IsComplete.realize_sentence_iff
∀ {L : FirstOrder.Language} {T : L.Theory},
T.IsComplete → ∀ (φ : L.Sentence) (M : Type u_1) [inst : L.Structure M] [M ⊨ T] [Nonempty M], M ⊨ φ ↔ T ⊨ᵇ φ- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 62
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.Formula.notproof · cited by 27
- FirstOrder.Language.Theory.IsCompletestatement and proof · cited by 11
- FirstOrder.Language.Sentence.realize_notproof · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentenceproof · cited by 5
- FirstOrder.Language.Theory.IsComplete.models_not_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.ACF_models_genericPolyMapSurjOnOfInjOn_of_primeproof · cited by 1
- ax_grothendieck_of_definableproof · cited by 1
- FirstOrder.Language.Theory.exists_modelType_is_realized_inproof · cited by 0