Talk:Kleene's recursion theorem

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First recursion theorem

I removed an "expert" tag from this section (ignoring whether the tag is well named). Not sure exactly what sort of accessibility is intended – the subsection of the SEP entry [1] does not even state the theorem, and overall is pretty content-free. This article is not the place for us to go into great depths about enumeration operators, any more than it is the place for us to go into details about computable functions. A longer description of enumeration operators could to go in the article on enumeration reducibility, which unfortunately does not exist. — Carl (CBM · talk) 02:07, 22 August 2009 (UTC)[reply]

It's true that SEP doesn't state the theorem (Odifreddi dumbed it down for a general audience there), but "Provides a basic tool to find explicit solutions to recursive equations, implicitly defining programs of recursive functions by circular definitions involving the program itself" as an introductory statement seems more accessible to me compared to "The first recursion theorem is related to fixed points determined by enumeration operators, which are a computable analogue of inductive definitions." You could introduce the operators in a 2nd sentence reserve the first for the reader that wants the general picture. By the way, {{intro-tooshort}} applies here too, but I won't tag it since you're probably reading this. I was trying to find some place to redirect recursive equation to that won't produce a big huh from the reader... Pcap ping 02:30, 22 August 2009 (UTC)[reply]