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Line 138: == Generalized theorem == In the context of his theory of numberings, [[Yury Yershov\|Ershov]] showed that Kleene's recursion theorem holds for any [[precomplete numbering]] ([[#CITEREFBarendregtTerwijn2019\|Barendregt & Terwijn 2019]],: p. 1151). A Gödel numbering is a precomplete numbering on the set of computable functions so the generalized theorem yields the Kleene recursion theorem as a special case (for an English survey see [[#CITEREFErshov1999\|Ershov 1999]],: pp. 473{{ndash}}503). Given a precomplete numbering <math>\nu</math> then for any partial computable function <math>f</math> with two parameters there exists a total computable function <math>t</math> with one parameter such that

Kleene's recursion theorem: Difference between revisions