The decomposability problem for torsion-free abelian groups is analytic-complete
The decomposability problem for torsion-free abelian groups is analytic-complete
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Providence, Rhode Island: American Mathematical Society
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English
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Providence, Rhode Island: American Mathematical Society
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We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is Σ30\Sigma ^0_3-complete. However, when we consider groups of infinite rank, it becomes Σ11\Sigma _1^1-complete, so it cannot be characterized by a first-order formula in the language of arithmetic.
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The decomposability problem for torsion-free abelian groups is analytic-complete
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TN_cdi_crossref_citationtrail_10_1090_proc_12509
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https://devfeature-collection.sl.nsw.gov.au/record/TN_cdi_crossref_citationtrail_10_1090_proc_12509
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0002-9939
E-ISSN
1088-6826
DOI
10.1090/proc/12509
