Stationary diamond at a regular cardinal
= Stationary diamond at a regular cardinal
{title2=$\Diamond_S\quad(S\subseteq\lambda=\operatorname{cf}(\lambda)>\omega)$}
A sequence $D_\alpha\subseteq\alpha$, indexed by a stationary <subset> $S$ of a regular uncountable <cardinal> $\lambda$, guesses every $X\subseteq\lambda$ stationarily often: $\{\alpha\in S:D_\alpha=X\cap\alpha\}$ is stationary. This extends the usual <stationary diamond principle> at $\omega_1$.