Talk:Rice–Shapiro theorem

Assessment
I'm the page author and I've assessed it as importance=Low (it's a relatively obscure topic, even if it is a relatively important theorem in computability theory. --Blaisorblade (talk) 20:19, 16 July 2008 (UTC)

Stewart Shapiro
There are various Shapiro, and I just guessed it was Stewart Shapiro the one involved with this theorem; there is (i.e. ) about this in the page, but I wanted to make the doubt clear. --Blaisorblade (talk) 20:19, 16 July 2008 (UTC)

Duplicate
As far as I could understand, this page explains the Rice's Theorem, which (the other) page is more detailed. Hence, I think this page could be deleted and redirect to Rice's Theorem one. --Guiraldelli (talk) 15:13, 8 September 2015 (UTC)

Saved paragraph from article
I moved the following paragraph from the article here for discussion as it makes no sense: (a) the set $$\{\theta:...\}$$ is a set of functions and has no notion of recursively enumerability and (b) $$n \in A$$ where $$n$$ is an integer but $$A$$ denotes a set of functions. Martin Ziegler (talk) 00:11, 3 March 2017 (UTC)

In general, one can obtain the following statement: The set $$\{n: \varphi_n \in A\}$$ is recursively enumerable iff the following two conditions hold:

(a) $$\{\theta: \theta = \varphi_n \forall  n \in A\}$$ is recursively enumerable;

(b) $$n \in A$$ iff $$\exists$$ a finite function $$\theta$$ such that  $$\varphi_n$$  extends $$\theta \wedge c(\theta) \in A$$  where $$c(\theta)$$  is the canonical index of  $$\theta$$.