You know what, you're right (and if I may add, on both counts ;-).
The wikipedia page I referenced, loosely summarized, is referring to an ordinal number with the cardinality aleph-1. The plain omega that I should have referenced has cardinality aleph-0.
Unfortunately, the ordinal I wanted does not have its own wikipedia page. WTF? Merely countable is not notable enough?
Some research project about a new language and the top comments are about how weird its name is and how the character looks like a butt? I'm speechless.
http://en.wikipedia.org/wiki/First_uncountable_ordinal
basically going as far as possible in the sequence C, C++, ...