The Isomorphism Problem for Computable Abelian p-Groups of Bounded Length

Journal of Symbolic Logic 70 (1):331 - 345 (2005)
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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DOI 10.2178/jsl/1107298523
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References found in this work BETA

Labelling Systems and R.E. Structures.C. J. Ash - 1990 - Annals of Pure and Applied Logic 47 (2):99-119.
The Isomorphism Problem for Classes of Computable Fields.Wesley Calvert - 2004 - Archive for Mathematical Logic 43 (3):327-336.
Back and Forth Relations for Reduced Abelian P-Groups.Ewan J. Barker - 1995 - Annals of Pure and Applied Logic 75 (3):223-249.

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Citations of this work BETA

Computable Abelian Groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
Scott Sentences for Certain Groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.
Index Sets for Some Classes of Structures.Ekaterina B. Fokina - 2009 - Annals of Pure and Applied Logic 157 (2-3):139-147.
Torsion-Free Abelian Groups with Optimal Scott Families.Alexander G. Melnikov - 2018 - Journal of Mathematical Logic 18 (1):1850002.

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