Let $X$ be a D11: Set.
Let $\mathcal{P}(X)$ be the D80: Power set of $X$.
A D11: Set $\mathcal{F} \subseteq \mathcal{P}(X)$ is the discrete sigma-algebra on $X$ if and only if \begin{equation} \mathcal{F} = \mathcal{P}(X) \end{equation}