In mathematics, and particularly in axiomatic set theory, the diamond principle ◊ is a combinatorial principle introduced by Ronald Jensen in Jensen (1972) that holds in the constructible universe (L) and that implies the continuum hypothesis.
Jensen extracted the diamond principle from his proof that the axiom of constructibility (V = L) implies the existence of a Suslin tree.
Jensen (1972) showed that the diamond principle ◊ implies the existence of Suslin trees.
Akemann & Weaver (2004) used ◊ to construct a C*-algebra serving as a counterexample to Naimark's problem.
Shelah (2010) proved that for κ > ℵ0, ◊κ+(S) follows from 2κ = κ+ for stationary S that do not contain ordinals of cofinality κ. Shelah showed that the diamond principle solves the Whitehead problem by implying that every Whitehead group is free.