Subtle Cardinal
In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number.
A cardinal κ is called subtle if for every closed and unbounded C ⊂ κ and for every sequence A of length κ for which element number δ (for an arbitrary δ), Aδ ⊂ δ there are α, β, belonging to C, with α<β, such that Aα=Aβ∩α. A cardinal κ is called ethereal if for every closed and unbounded C ⊂ κ and for every sequence A of length κ for which element number δ (for an arbitrary δ), Aδ ⊂ δ and Aδ has the same cardinal as δ, there are α, β, belonging to C, with α<β, such that card(α)=card(Aβ∩Aα).
Subtle cardinals were introduced by Jensen & Kunen (1969). Ethereal cardinals were introduced by Ketonen (1974). Any subtle cardinal is ethereal, and any strongly inaccessible ethereal cardinal is subtle.
Read more about Subtle Cardinal: Theorem
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