Stationary-indexed club principle
= Stationary-indexed club principle
{title2=$\clubsuit_S$}
For a stationary $S\subseteq\omega_1$, there are cofinal ladders $A_\delta\subset\delta$ of order type $\omega$, indexed by <limit ordinals> in $S$, such that every uncountable $X\subseteq\omega_1$ contains one of these ladders. This predicts a contained ladder, whereas <stationary diamond principle> predicts a whole initial segment.