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== History ==
[[Recursive definition]]s had been used more or less formally in mathematics before, but the construction of primitive recursion is traced back to [[Richard Dedekind]]'s theorem 126 of his ''Was sind und was sollen die Zahlen?'' (1888). This work was the first to give a proof that a certain recursive construction defines a unique function.<ref name="Smith2013">{{cite book|author=Peter Smith|title=An Introduction to Gödel's Theorems|year=2013|publisher=Cambridge University Press|isbn=978-1-107-02284-3|pages=98–99|edition=2nd |url=https://www.logicmatters.net/igt/}}</ref><ref name="Tourlakis2003">{{cite book|author=George Tourlakis|title=Lectures in Logic and Set Theory: Volume 1, Mathematical Logic|year=2003|publisher=Cambridge University Press|isbn=978-1-139-43942-8|page=129}}</ref><ref name="Downey2014">{{cite book|editor=Rod Downey|title=Turing's Legacy: Developments from Turing's Ideas in Logic|year=2014|publisher=Cambridge University Press|isbn=978-1-107-04348-0|page=474}}</ref>
[[Primitive recursive arithmetic]] was first proposed by [[Thoralf Skolem]]<ref>[[Thoralf Skolem]] (1923) "The foundations of elementary arithmetic" in [[Jean van Heijenoort]], translator and ed. (1967) ''From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931''. Harvard Univ. Press: 302-33.</ref> in 1923.
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