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