Theorems · Definition · logic and foundations
FirstOrder.Language.Sentence.Realize
{L : FirstOrder.Language} → (M : Type w) → [L.Structure M] → L.Sentence → PropA sentence can be evaluated as true or false in a structure.
- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Formula.Realizeproof · cited by 81
Cited by65
Results whose statement or proof uses this declaration.
- FirstOrder.Language.completeTheoryproof · cited by 14
- FirstOrder.Language.Theory.realize_sentence_of_memstatement · cited by 11
- FirstOrder.Language.Theory.models_sentence_iffstatement · cited by 6
- FirstOrder.Language.Sentence.realize_notstatement · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentencestatement and proof · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiableproof · cited by 4
- FirstOrder.Language.elementarilyEquivalent_iffstatement and proof · cited by 4
- FirstOrder.Language.Formula.realize_equivSentence_symm_constatement and proof · cited by 4
- FirstOrder.Language.Theory.Model.realize_of_memstatement · cited by 3
- FirstOrder.Language.Theory.model_iffstatement and proof · cited by 3
- FirstOrder.Language.LHom.onTheory_modelproof · cited by 3
- FirstOrder.Language.Formula.realize_equivSentence_symmstatement · cited by 3