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The stationary-indexed club principle ${♣}_S$ asserts a sequence $⟨A_{\delta }:\delta \in S\cap \mathrm{Lim}({\omega }_1)⟩$ with each $A_{\delta }\subset \delta$ cofinal of order type $\omega$, such that for every uncountable $X\subseteq {\omega }_1$ some $\delta \in S$ satisfies $A_{\delta }\subseteq X$. It predicts a cofinal ladder contained in the target, rather than predicting the entire initial segment of the target as diamond does. For a stationary $S$ with successor members, only its stationary limit-ordinal part is relevant; countable limit ordinals have cofinality $\omega$. This is the restricted version of the club principle.

The club principle $♣$ asserts that there is a sequence $⟨A_{\delta }:\delta \in \mathrm{Lim}({\omega }_1)⟩$ such that $A_{\delta }\subseteq \delta$ has order type $\omega$, is cofinal in $\delta$, andIt guesses a cofinal countable subset of an uncountable set, with inclusion as the guessing requirement.