Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence \begin{equation} X, \quad \mathcal{P}(X), \quad \mathcal{P}(\mathcal{P}(X)), \quad \mathcal{P}(\mathcal{P}(\mathcal{P}(X))), \quad \ldots \end{equation}

Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence \begin{equation} \mathcal{P}^0(X), \quad \mathcal{P}^1(X), \quad \mathcal{P}^2(X), \quad \mathcal{P}^3(X), \quad \ldots \end{equation}

Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence \begin{equation} X, \quad \mathcal{P} X, \quad \mathcal{P} \mathcal{P} X, \quad \mathcal{P} \mathcal{P} \mathcal{P} X, \quad \ldots \end{equation}