Not to be too pedantic, but little omega is not the first uncountable ordinal (it is countable by definition), it is the first infinite one.
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?