 Systematic consideration of such alternative recursion schemes exemplified by (\ref{pidef}) was initiated by Péter (1932). It was also she who introduced the term “primitive recursive” to describe the class of functions given by Gödel’s scheme (\ref{gprimrec}), a choice which would become standard after its adoption by Kleene (1936a). Péter additionally showed that Hilbert’s (1926) formulation of “ordinary recursion” is equivalent to primitive recursion, and that the primitive recursive functions are closed under course of values recursion, as well as so-called nested recursions of one variable. Such studies led to her book (Péter 1967), whose original German edition Rekursive Funktionen (1951) was the first monograph devoted to recursive functions. Together with the later work of Grzegorczyk (1953), these developments also inspired the investigation of various subrecursive hierarchies which would later play a role in proof theory and computer science.[10] 