 Overall Skolem considered instances of what we would now refer to as primitive recursion, course of values recursion, double recursion, and recursion on functions of type \(\mathbb{N} \rightarrow \mathbb{N}\). He did not, however, introduce general schemas so as to systematically distinguish these modes of definition. Nonetheless, properties i–iv of Skolem’s treatment provide a means of assimilating calculations like (\ref{factcalc}) to derivations in quantifier-free first-order logic.  It is thus not difficult to discern in (Skolem 1923) the kernel of the system we now know as Primitive Recursive Arithmetic (as later formally introduced by Hilbert &amp; Bernays 1934, ch. 7).