Diagonal halting set
= Diagonal halting set
{title2=$K$}
For an effective enumeration of unary partial computable functions, the diagonal halting set is
$$
K=\{e:f_{e,1}(e)\text{ is defined}\}.
$$
Equivalently, for an enumeration $W_e$ of computably enumerable sets, $K=\{e:e\in W_e\}$.