Theorems · Definition · logic and foundations
FirstOrder.Language.Theory.IsSatisfiable
{L : FirstOrder.Language} → L.Theory → PropA theory is satisfiable if a structure models it.
- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Theorystatement and proof · cited by 154
- FirstOrder.Language.Theory.ModelTypeproof · cited by 62
Cited by28
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsCompleteproof · cited by 11
- FirstOrder.Language.Theory.IsMaximalproof · cited by 10
- FirstOrder.Language.Theory.IsSatisfiable.monostatement and proof · cited by 7
- FirstOrder.Language.Theory.Model.isSatisfiablestatement · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiablestatement and proof · cited by 4
- FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiablestatement · cited by 3
- Cardinal.Categorical.isCompletestatement and proof · cited by 3
- FirstOrder.Language.Theory.CompleteType.setOfPred_subset_eq_empty_iffstatement and proof · cited by 3
- FirstOrder.Language.Theory.IsFinitelySatisfiableproof · cited by 2
- FirstOrder.Language.Theory.IsMaximal.mem_of_modelsproof · cited by 2
- FirstOrder.Language.Theory.isSatisfiable_directed_union_iffstatement and proof · cited by 1
- FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheorystatement and proof · cited by 1