Infinite-domain index set

For an effective enumeration $f_{w,1}$ of unary partial computable functions,is an index set.

For a nonempty set $X$ of words, the propertyis a nontrivial extensional property of unary partial computable functions: the nowhere-defined function fails it, while any total constant function with value in $X$ satisfies it. The Rice theorem therefore makes its index set undecidable.