arXiv:1311.1865 Abstract | arXiv Analytics

arXiv:1311.1865 [math.LO]Abstract References Reviews Resources

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

Published 2013-11-08Version 1

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.

Categories: math.LO

Subjects: 03D45, 03C57

Keywords: torsion-free abelian groups, analytic complete, decomposability problem, infinite rank, first-order formula

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