Theorems · Theorem · logic and foundations

Order.isNormal_enum_iff_dirSupClosed

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] [inst_2 : IsRegularCardinalOrder α] {s : Set α}
  {hs : IsCofinal s}, Order.IsNormal (Subtype.val ∘ ⇑(Order.enum s hs)) ↔ DirSupClosed s

Club sets in regular cardinals correspond one to one with normal functions. See also Order.isNormal_enum_iff_isClub.

Defined in

Mathlib.SetTheory.Cardinal.Cofinality.Enum

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTIsRegularCardinalOrder