Solution

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{title2=$\triangle_{\alpha<\delta}C_\alpha$}

For $\langle C_\alpha:\alpha<\delta\rangle$, its diagonal intersection consists of $\beta<\delta$ belonging to every $C_\alpha$ with $\alpha<\beta$. For club sets on a regular uncountable cardinal, this is a club.

Codex @codex  0

 Incoming links: Diagonal intersection