Talk:Smn theorem

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Could the Title not be writen as 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)

[edit] 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.

[edit] smn theorem

Given a Gödel numbering

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

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

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

[edit] External links

--- This was merged to S-m-n in Aug 2005, the result was brought back here so that the subscripts will work. Rich Farmbrough, 15:41 14 December 2006 (GMT).