Diamond principle

Summary

The diamond principle, written $\diamondsuit$, is a combinatorial axiom about $\omega_1$ introduced by Ronald Jensen. It says that a sequence of guesses, one at each countable ordinal, correctly predicts every subset of $\omega_1$ on a stationary set of ordinals. It holds in the constructible universe, and it implies the continuum hypothesis. It is used to build objects such as Suslin trees, and the precise definition is given separately.