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This is a list of order types, sorted by the set inclusion relation and by cardinality.

Finite Edit

These ordinals have a cardinality of less than aleph null.

Countably Infinite Edit

These ordinals have a cardinality equal to aleph null.

Uncountable Edit

These ordinals have a cardinality greater than or equal to aleph one.

Non-Ordinal, Greater Than Aleph OneEdit

• $\alpha_p$ and $\alpha^{+}_p$ where p has a cardinality greater than $\aleph_2$