Theorems · Definition · logic and foundations
FirstOrder.Language.Theory.ModelsBoundedFormula
{L : FirstOrder.Language} → L.Theory → {α : Type w} → {n : ℕ} → L.BoundedFormula α n → PropA theory models a (bounded) formula when any of its nonempty models realizes that formula on all inputs.
- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Theory.ModelTypeproof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
Cited by33
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.Iffproof · cited by 32
- FirstOrder.Language.Theory.Impproof · cited by 16
- FirstOrder.Language.Theory.IsCompleteproof · cited by 11
- FirstOrder.Language.Theory.models_sentence_iffstatement · cited by 6
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentencestatement and proof · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiablestatement · cited by 4
- Cardinal.Categorical.isCompleteproof · cited by 3
- FirstOrder.Language.Theory.models_sentence_of_memstatement · cited by 3
- FirstOrder.Language.Theory.IsComplete.realize_sentence_iffstatement and proof · cited by 3
- FirstOrder.Language.Theory.IsMaximal.mem_iff_modelsstatement · cited by 3
- FirstOrder.Language.Theory.models_formula_iffstatement · cited by 2
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formulastatement and proof · cited by 2