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A much more common notation for Ω as the first uncountable ordinal number is ω1
The article defines an ordinal as a set whose every element is a subset; but {0,1,{1}} is such a set, and is not an ordinal. To be an ordinal, the set should have the additional property of being totally ordered by containment. (Then the axiom of foundation yields that the set is well-ordered.)
- Thanks for catching this! --AxelBoldt