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Theories of classication distinguish classes with some good struc- ture theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classiable in general, but are classiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classiable classes from non- classiable. In this paper, we calculate the degree of the isomorphism problem for Abelianp-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are conal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated.

The isomorphism problem for computable Abelian p-groups of bounded length

The isomorphism problem for computable Abelian _p-groups of bounded length