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

Published online by Cambridge University Press:  12 March 2014

Wesley Calvert*
Affiliation:
Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame, Indiana 46556, USA, E-mail: wcalvert@nd.edu

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2005

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