'''Primitive recursive arithmetic''', or ('''PRA''',) is a [[Quantification (logic)|quantifier]]-free formalization of the [[natural numbers]]. It was first proposed by [[Thoralf Skolem|Skolem]]<ref>{{citation|first=Thoralf|last=Skolem|authorlink=Thoralf Skolem|year=1923|title=Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsbereich|trans-title=The foundations of elementary arithmetic established by means of the recursive mode of thought without the use of apparent variables ranging over infinite domains|language=German|url=https://www.ucalgary.ca/rzach/files/rzach/skolem1923.pdf|journal=Skrifter utgit av Videnskapsselskapet i Kristiania. I, Matematisk-naturvidenskabelig klasse|volume=6|pages=1–38}}. Reprinted in translation in {{citation
| last = van Heijenoort | first = Jean | author-link = Jean van Heijenoort
