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, &omega;&omega; has cofinality &omega;, but one of its club subsets is {&alpha;|&omega;0 < &alpha; < &omega;1} &cup; {&omega;&beta;|&beta; < &omega;} which has cardinality &aleph;1. JRSpriggs (talk) 01:32, 5 June 2021 (UTC)