\(MC(\infty,\infty,\mathrm{odd})\): 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.

\(MC(\infty,\infty)\) \((MC)\), The Axiom of Multiple Choice: For every set \(M\) of non-empty sets there is a function \(f\) such that \((\forall x\in M)(\emptyset\neq f(x)\subseteq x\) and \(f(x)\) is finite).

Every set is almost well orderable.

There does not exist an infinite, compact connected \(p\) space. (A \(p\) space is a \(T_2\) space in which the intersection of any well orderable family of open sets is open.)