Countable-family diamond principle
= Countable-family diamond principle
{title2=$\Diamond'_S$}
At each $\alpha\in S$, a countable family $E_\alpha\subseteq\mathcal P(\alpha)$ is supplied. Every $X\subseteq\lambda$ has $X\cap\alpha\in E_\alpha$ on a stationary <subset> of $S$. The <countable-family diamond equivalence> shows that this apparently weaker prediction is equivalent to a single diamond guess at each index.