Two linear orderings are equimorphic if each can be embedded into
the other.
We prove that every hyperarithmetic linear ordering is equimorphic to a
recursive one.
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On the way to our main result we prove that a linear ordering has
Hausdorff rank less than ω₁CK if and only if it is equimorphic to
a recursive one.
As a corollary of our proof we prove that, given a recursive ordinal
α, the partial ordering of equimorphism types of linear orderings
of Hausdorff rank at most α ordered by embeddablity is
recursively presentable.