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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) reply

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

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) reply

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

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

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

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