Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Formulation 0
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}
Formulation 1
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}
Child definitions
» D1727: Boolean algebra
» D2150: Intersection algebra
» D2149: Lambda algebra
» D5143: Set partition
» D3369: Subset structure
» D86: Topology