 Principle of Dependent Choices (Bernays 1942, Tarski 1948). For any nonempty relation \(R\) on a set \(A\) for which \(\range(R) \subseteq \domain(R)\), there is a function \(f: \omega \rightarrow A\) such that, for all \(n\in \omega, R(f(n),f(n+1))\). This principle, although (much) weaker than AC, cannot be proved without it in the context of the remaining axioms of set theory. 