#### Abstract

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable 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 classifiable classes from non-classifiable. In this paper, we calculate the degree of the isomorphism problem for Abelian _{ p }-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are cofinal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated.

#### Recommended Citation

Calvert, Wesley.
"The isomorphism problem for computable Abelian p-groups of bounded length."
*Journal of Symbolic Logic*
70, No. 1
(Mar 2005): 331--345.
doi:10.2178/jsl/1107298523.