If is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to is called its index set. If the index set of is a recursive set, then either is empty or contains all recursively enumerable sets.

Rice's theorem is an important result for computer science because it sets up boundaries for research in that area. It basically states that only trivial properties of programs are algorithmically decidable.

This entry contributed by Alex Sakharov (author's link)

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Sakharov, Alex. "Rice's Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RicesTheorem.html