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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The decomposability problem for torsion-free abelian groups is analytic-complete
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by Kyle Riggs PDF
Proc. Amer. Math. Soc. 143 (2015), 3631-3640 Request permission

Abstract:

We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $\Sigma ^0_3$-complete. However, when we consider groups of infinite rank, it becomes $\Sigma _1^1$-complete, so it cannot be characterized by a first-order formula in the language of arithmetic.
References
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Additional Information
  • Kyle Riggs
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • Address at time of publication: Department of Mathematics, Eastern Washington University, Cheney, WA 99004
  • Email: kriggs3@ewu.edu
  • Received by editor(s): April 2, 2013
  • Received by editor(s) in revised form: November 2, 2013
  • Published electronically: April 6, 2015
  • Additional Notes: The author would like to thank Steffen Lempp and Alexander Melnikov for their fruitful discussions.
  • Communicated by: Mirna Dz̆amonja
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3631-3640
  • MSC (2010): Primary 03D45, 03C57
  • DOI: https://doi.org/10.1090/proc/12509
  • MathSciNet review: 3348804