Alpha order types

The alpha order types are a collection of order types. For an order type p, $$\alpha_p$$ is the order type of alphabetical order using a collection of characters with order type p. Unless p is finite, $$\alpha_p$$ has the same cardinality as p. If p is finite, $$\alpha_p$$ has order type $$\aleph_0$$. Alpha order types are related to alpha-plus order types.