Theorems · Definition · logic and foundations
FirstOrder.Language.Theory.typesWith
{L : FirstOrder.Language} → {α : Type w} → (T : L.Theory) → (L.withConstants α).Sentence → Set (T.CompleteType α)The clopen set of complete types which contain a formula.
- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- FirstOrder.Language.Theory.CompleteTypestatement and proof · cited by 35
- FirstOrder.Language.Theory.CompleteType.toTheoryproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- CompleteType.isOpen_typesWithstatement · cited by 2
- CompleteType.isClosed_typesWithstatement · cited by 1
- FirstOrder.Language.Theory.CompleteType.typesWith_infstatement and proof · cited by 1
- FirstOrder.Language.Theory.CompleteType.typesWith_notstatement · cited by 1
- FirstOrder.Language.Theory.CompleteType.typesWith_topstatement · cited by 1
- CompleteType.isClopen_typesWithstatement · cited by 0
- CompleteType.isTopologicalBasis_range_typesWithstatement and proof · cited by 0
- FirstOrder.Language.Theory.CompleteType.mem_typesWith_iffstatement · cited by 0