Category:Von Neumann Hierarchy

From ProofWiki
Jump to navigation Jump to search

This category contains results about Von Neumann Hierarchy.

Let $U$ denote the universal class.

The von Neumann hierarchy is a mapping $V: \On \to U$ on the ordinals, defined via transfinite recursion:

$\map V x = \begin{cases} \O & : x = 0 \\ & \\ \powerset {\map V n} & : x = n^+ \\ & \\ \displaystyle \bigcup_{y \mathop \in x} \map V y & : x \in \operatorname {Lim} \\ \end{cases}$


$\powerset x$ denotes the power set of $x$
$\operatorname {Lim}$ denotes the set of limit ordinals.