ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Definition D5464
Hyperpower set sequence
Formulation 0
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}
Formulation 1
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}
Formulation 2
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}
Children
D4075: Hyperpower set
D673: Von Neumann ordinal sequence