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March 2005 The isomorphism problem for computable Abelian p-groups of bounded length
Wesley Calvert
J. Symbolic Logic 70(1): 331-345 (March 2005). DOI: 10.2178/jsl/1107298523

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.

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Wesley Calvert. "The isomorphism problem for computable Abelian p-groups of bounded length." J. Symbolic Logic 70 (1) 331 - 345, March 2005. https://doi.org/10.2178/jsl/1107298523

Information

Published: March 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1099.03031
MathSciNet: MR2052886
Digital Object Identifier: 10.2178/jsl/1107298523

Subjects:
Primary: 03C57 , 03D45 , 20K10

Keywords: Back-and-forth , ‎classification‎ , Computable , Ulm

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 1 • March 2005
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