Zermelo-Fraenkel Set Theory

Axiom: Axiom of Power Set (Ernst Zermelo, 1908)

For each set \(X\) exist a set \(Y\) such that it contains \(X\) and all of its subsets, including the empty set.

\[\forall X~\exists~Y~\forall Z~(Z\in Y\Longrightarrow Z\subseteq Y).\]

References

[656] Hoffmann, Dirk W.: “Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

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