ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Subset
▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
▼ Subset structure
Definition D5638
Top subset structure of natural numbers
Formulation 0
An D548: Ordered pair $M = (\mathbb{N}, \mathcal{P}(\mathbb{N}))$ is the top subset structure of natural numbers if and only if
(1) $\mathbb{N}$ is the D225: Set of natural numbers
(2) $\mathcal{P}(\mathbb{N})$ is a D80: Power set for $\mathbb{N}$