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

Kyle Riggs

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arXiv · 1311.1865

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

Kyle Riggs

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Abstract

We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $Σ^0_3$-complete. However, when we consider groups of infinite rank, it becomes $Σ^1_1$-complete, so it cannot be characterized by a first-order formula in the language of arithmetic.

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Kyle Riggs. 2013-11-08. The decomposability problem for torsion-free abelian groups is analytic complete. https://arxiv.org/abs/1311.1865

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