Subtle cardinal (original) (raw)
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 exist α, β, belonging to C, with α < β, such that Aα = Aβ ∩ α. Subtle cardinals were introduced by . Ethereal cardinals were introduced by . Any subtle cardinal is ethereal, and any strongly inaccessible ethereal cardinal is subtle.
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| dbo:abstract | 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 exist 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 exist α, β, belonging to C, with α < β, such that card(α) = card(Aβ ∩ Aα). Subtle cardinals were introduced by . Ethereal cardinals were introduced by . Any subtle cardinal is ethereal, and any strongly inaccessible ethereal cardinal is subtle. (en) |
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| rdfs:comment | 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 exist α, β, belonging to C, with α < β, such that Aα = Aβ ∩ α. Subtle cardinals were introduced by . Ethereal cardinals were introduced by . Any subtle cardinal is ethereal, and any strongly inaccessible ethereal cardinal is subtle. (en) |
| rdfs:label | Subtle cardinal (en) |
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