Solution
= Solution
For an effective enumeration $(W_w)_{w\in\mathbb W}$ of the computably enumerable languages, the diagonal <halting problem> is
$$
\boxed{\mathbf K=\{w\in\mathbb W:w\in W_w\}}.
$$
Equivalently, if $f_{w,1}$ is the unary partial function coded by $w$, then
$$
w\in\mathbf K
\quad\Longleftrightarrow\quad
f_{w,1}(w)\mathbin\downarrow.
$$
\b[Thus $\mathbf K$ is the <diagonal halting set>.]