# Talk:Smn theorem

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## Title

Could the Title not be writen as ${\displaystyle s_{n}^{m}}$ ?

I don't think so - due to technical restrictions sub- and superscripts are not presently possible. --Kizor 12:07, 24 November 2005 (UTC)

## merged version by Math MArtin

In computability theory the smn theorem, Kleene's s-m-n Theorem or translation lemma is a basic result about computable functions first given by Stephen Cole Kleene.

### smn theorem

Given a Gödel numbering

${\displaystyle \phi :\mathbb {N} \to \mathbf {P} ^{(1)}}$

of the computable functions with one parameter then for every computable function ${\displaystyle f}$ with two parameters ${\displaystyle f\in \mathbf {P} ^{(2)}}$ there exists a total computable function ${\displaystyle \phi (i)\in \mathbf {R} ^{(1)}}$ so that

${\displaystyle f(i,x)=\phi (r(i))(x)\quad i,n\in \mathbb {N} }$