If there is a recursive function$$f(x) = \begin{cases}1 & \text{if $x \notin A$}\\\text{undefined} & \text{if $x \in A$}\\\end{cases}$$Is there a special name for the class of sets like $A$?
Is there a name for complement of recursively enumerable set?
terminology;computability;undecidability
The complement of a recursively enumerable (RE) language is called co-recursively enumerable (co-RE).As RE and co-RE form the first level of the arithmetic hierarchy, they are also known by aliases $\Sigma_1^0$ and $\Pi_1^0$.