Definition (Sequential covering class)

Let $X$ be a set. We say that $\mathcal{K}\subseteq 2^{X}$ is a sequential covering class of $X$ if and only if

1. $$\emptyset\in\mathcal{K}$$
2. $$\forall A\subseteq X,\ \exists(E_{k})_{k\ge 1}\subseteq \mathcal{K}:A\subseteq \cup_{k=1}^{\infty}E_{k}$$