Every quotient group of an Abelian group each of whose elements has order  \(\le n\) has a set of representatives.

\(MC(\infty,\infty,\mathrm{odd})\): For every set \(X\) of  sets such that for all \(x\in X\), \(|x|\ge 1\), there is a function \(f\) such that  for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\) and \(|f(x)|\) is odd.

  \(C(\infty ,2)\):  Every family of pairs has a choice function.

Let \(\Omega\) be the set of all (undirected) infinite cycles of reals (Graphs whose vertices are real numbers, connected, no loops and each vertex adjacent to  exactly two others). Then there is a function \(f\) on \(\Omega \) such that for all \(s\in\Omega\), \(f(s)\) is a direction along \(s\).