How can I compute the number of clubs (closed unbounded subsets) of a cardinal $\kappa$? I feel like there should $\kappa$ many of them but I am a bit lost about how to prove it...
2026-04-08 10:14:15.1775643255
Number of clubs in a cardinal
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Let $$\kappa=L\cup S$$ where $L$ is the set of limit ordinals, and $S$ of successor ordinals. Then for eaxh $X\subseteq S$, $$L\cup X$$ is a club.