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Do I gather correctly that the cardinality of a club set in κ is the same as the cofinality of κ? -- Trɔpʏliʊm • blah 16:40, 27 March 2021 (UTC) reply

That would be a nice question to ask at the mathematics reference desk. -- Trovatore ( talk) 17:24, 27 March 2021 (UTC) reply

No. The cofinality of an unbounded subset of κ is the same as the cofinality of κ. However, ω_ω has cofinality ω, but one of its club subsets is {α|ω₀ < α < ω₁} ∪ {ω_β|β < ω} which has cardinality ℵ₁. JRSpriggs ( talk) 01:32, 5 June 2021 (UTC) reply