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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1107298523
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 49,040
Through your library

References found in this work BETA

Countable Algebra and Set Existence Axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
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.

View all 7 references / Add more references

Citations of this work BETA

Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
Computable Abelian Groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Scott Sentences for Certain Groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.
Torsion-Free Abelian Groups with Optimal Scott Families.Alexander G. Melnikov - 2018 - Journal of Mathematical Logic 18 (1):1850002.
PAC Learning, VC Dimension, and the Arithmetic Hierarchy.Wesley Calvert - 2015 - Archive for Mathematical Logic 54 (7-8):871-883.

View all 6 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2010-08-24

Total views
15 ( #605,933 of 2,311,025 )

Recent downloads (6 months)
1 ( #753,261 of 2,311,025 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature