Stationary diamond principle (${♢}_S$)

For a stationary $S\subseteq {\omega }_1$, a sequence $D_{\alpha }\subseteq \alpha$ indexed by $S$ guesses every $X\subseteq {\omega }_1$ on a stationary subset of $S$.

At a correctly guessing limit stage of a normal tree construction, make every new level node extend a member of the guessed maximal tree antichain. It follows that the antichain has no later member. This produces a Suslin tree from the stationary diamond principle.