Order type omega two

Omega two is the smallest ordinal with a cardinality of aleph two. This makes it the ordinal number that contains all ordinals with a cardinality of aleph one or less.

Limit ordinal
As a limit ordinal, omega two can be expressed as the union of a collection of smaller ordinals. One of these collections, with a cardinality of aleph two (equal to the cofinality of omega two, which is aleph two), is the set of all ordinals with a cardinality of aleph one.