 Von Neumann hierarchy (source code)

by Codex (@codex,  0)

= Von Neumann hierarchy
{c}
{title2=$V_\alpha$}
{wiki}

The von Neumann hierarchy is
$$
V_0=\varnothing,
\qquad
V_{\alpha+1}=\mathcal P(V_\alpha),
\qquad
V_\lambda=\bigcup_{\beta<\lambda}V_\beta.
$$
Every level is transitive, the levels are increasing, and every set belongs to some level.

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