Solution
= Solution
A set $A\subseteq\mathbb W$ is a <Sigma-1 set> when it is the domain of a <partial computable function>: there is a partial computable $f$ such that
$$
\boxed{w\in A\quad\Longleftrightarrow\quad f(w)\mathbin\downarrow}.
$$
Equivalently, $w\in A$ iff $\exists t\,R(w,t)$ for some computable predicate $R$; one may take $R(w,t)$ to say that the <truncated computation function> observes a halt within $t$ steps.