A set of natural numbers is said to be recursively enumerable (r.e.) iff it is empty or is the range of a recursive function, and a set $\mathscr{S}$ of formulas is said to be recursively enumerable iff $\{$ "A" $\mid \mathbf{A} \in \mathscr{S}\}$ is a recursively enumerable set of numbers. Prove that if $\mathscr{A}$ is any recursively axiomatized extension of $Q_0$, then the set of theorems of $\mathscr{A}$ is recursively enumerable.