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Theorems · Theorem · logic and foundations

CompleteType.isOpen_typesWith

∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type u_1} (φ : (L.withConstants α).Sentence), IsOpen (T.typesWith φ)
Defined in
Mathlib.ModelTheory.Topology.Types
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CompleteType.isClosed_typesWith · cited by 1CompleteType.isClosed_typ…CompleteType.isClopen_typesWith · cited by 0CompleteType.isClopen_typ…IsOpen · cited by 2400IsOpenFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Theory.CompleteType · cited by 35Theory.CompleteTypeTopologicalSpace.isOpen_generateFrom_of_mem · cited by 11TopologicalSpace.isOpen_g…FirstOrder.Language.Theory.typesWith · cited by 9Theory.typesWithCompleteType.isOpen_typesWithCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.