Rice–Shapiro theorem

In computability theory, the Rice–Shapiro theorem is a generalization of Rice's theorem, and is named after Henry Gordon Rice and Norman Shapiro.

Let A be a set of partial-recursive unary functions on the domain of natural numbers such that the set ${\displaystyle Ix(A):=\{n\mid \varphi _{n}\in A\}}$ is recursively enumerable, where ${\displaystyle \varphi _{n}}$ denotes the ${\displaystyle n}$-th partial-recursive function in a Gödel numbering.

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