Theorems · Inductive type · logic and foundations
FirstOrder.Language.Theory.CompleteType
{L : FirstOrder.Language} → L.Theory → Type w → Type (max (max u v) w)A complete type over a given theory in a certain type of variables is a maximally consistent (with the theory) set of formulas in that type.
- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.Theorystatement · cited by 154
Cited by45
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.typesWithstatement and proof · cited by 9
- FirstOrder.Language.Theory.CompleteType.isMaximalstatement and proof · cited by 8
- FirstOrder.Language.Theory.CompleteType.subsetstatement and proof · cited by 4
- FirstOrder.Language.Theory.typeOfstatement · cited by 3
- FirstOrder.Language.Theory.CompleteType.compl_setOfPred_memstatement and proof · cited by 3
- FirstOrder.Language.Theory.CompleteType.setOfPred_subset_eq_empty_iffstatement and proof · cited by 3
- CompleteType.isOpen_typesWithstatement · cited by 2
- FirstOrder.Language.Theory.CompleteType.mem_or_not_memstatement and proof · cited by 2
- FirstOrder.Language.Theory.CompleteType.toTheorystatement and proof · cited by 2
- CompleteType.isClosed_typesWithstatement and proof · cited by 1
- FirstOrder.Language.Theory.realizedTypesstatement · cited by 1
- FirstOrder.Language.Theory.CompleteType.iInter_setOfPred_subsetstatement and proof · cited by 1