Talk:Club set

cofinality?

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)

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

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)