 Exactly the same is true of the set of formulae that are derivable in a formalized deductive calculus. A formula \(F\) is derivable in a Fregean calculus \(C\) just in case \(F\) is obtainable from the axioms of \(C\) after some finite series of applications of the rules of inference of \(C\). But the axioms are certain formulae built by the process of grammatical formation, so they can be seen as (or codified by) certain numbers; and the rules of inference can again be seen as (or codified by) certain computable arithmetical operations. So the derivable formulae can be seen as (or codified by) the numbers obtainable from the axiom numbers after some finite series of applications of the inference operations, and thus their set is again characterizable in terms of concepts of standard mathematics (again arithmetic suffices).