{"paper":{"title":"The complexity of the embeddability relation between torsion-free abelian groups of uncountable size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Filippo Calderoni","submitted_at":"2017-04-11T16:13:58Z","abstract_excerpt":"We prove that for every uncountable cardinal $\\kappa$ such that $\\kappa^{<\\kappa}=\\kappa$, the quasi-order of embeddability on the $\\kappa$-space of $\\kappa$-sized graphs Borel reduces to the embeddability on the $\\kappa$-space of $\\kappa$-sized torsion-free abelian groups. Then we use the same techniques to prove that the former Borel reduces to the embeddability on the $\\kappa$-space of $\\kappa$-sized $R$-modules, for every $\\mathbb{S}$-cotorsion-free ring $R$ of cardinality less than the continuum. As a consequence we get that all the previous are complete $\\boldsymbol{\\Sigma}^1_1$ quasi-or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03392","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}