Let $X$ be a D11: Set.
Let $\mathcal{P}(X)$ be the D80: Power set of $X$.
A D11: Set $\mathcal{S}$ is a subset algebra on $X$ if and only if
\begin{equation}
\mathcal{S} \subseteq \mathcal{P}(X)
\end{equation}
Let $X$ be a D11: Set.
Let $\mathcal{P}^2(X)$ be a D4075: Hyperpower set of $X$.
A D11: Set $\mathcal{S}$ is a subset algebra on $X$ if and only if
\begin{equation}
\mathcal{S} \in \mathcal{P}^2(X)
\end{equation}
