The decomposability problem for torsion-free abelian groups is analytic complete

Kyle Riggs

The decomposability problem for torsion-free abelian groups is analytic complete

Logic 2013-11-11 v1

Authors: Kyle Riggs

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.

Keywords

group theory abelian groups finite group theory

Cite

@article{arxiv.1311.1865,
  title  = {The decomposability problem for torsion-free abelian groups is analytic complete},
  author = {Kyle Riggs},
  journal= {arXiv preprint arXiv:1311.1865},
  year   = {2013}
}

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