Transitive Set - Examples

Examples

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 Vα and Lα leading to the construction of the von Neumann universe V and Gödel's constructible universe L are transitive sets. The universes L and V themselves are transitive classes.

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