axiom of countable choice noun1 •A weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.we have no way to infer ∃R∀n[P0n→∀x(R_nx→Fx)∧n=Nx:R_nx)] without an axiom of countable choice. — 2012
