**subset structure**if and only if

(1) | $X$ is a D11: Set |

(2) | $\mathcal{S} \subseteq \mathcal{P}(X)$ (D3367: Subset algebra) |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

Formulation 0

An D548: Ordered pair $S = (X, \mathcal{S})$ is a **subset structure** if and only if

(1) | $X$ is a D11: Set |

(2) | $\mathcal{S} \subseteq \mathcal{P}(X)$ (D3367: Subset algebra) |

Also known as

Hypergraph

Child definitions