 Theorem 5.2 For any true \(\Pi^0_1\) sentence F a number \(a_{F}\in{\cO}\) can be constructed such that \({{\mid}\,{a_{F}}\,{\mid}}=\omega+1\) and \(\bT_{a_{F}}\vdash F\). Moreover, the function \(F\mapsto a_{F}\) is given by a primitive recursive function.