High Quality Content by WIKIPEDIA articles! Using the definition of ordinal numbers suggested by John von Neumann, ordinal numbers are defined as hereditarily transitive sets: an ordinal number is a transitive set whose members are also transitive (and thus ordinals). Any of the stages V? and L? leading to the construction of the von Neumann universe V and Godel's constructible universe L are transitive sets. The universes L and V themselves are transitive classes.

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