{"paper":{"title":"Torsion-free abelian groups of finite rank and fields of finite transcendence degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Julia Knight, Meng-Che \"Turbo\" Ho, Russell Miller","submitted_at":"2024-03-04T21:16:54Z","abstract_excerpt":"Let $\\operatorname{TFAb}_r$ be the class of torsion-free abelian groups of rank $r$, and let $\\operatorname{FD}_r$ be the class of fields of characteristic $0$ and transcendence degree~$r$. We compare these classes using various notions. Considering Scott complexity of the structures in the classes and the complexity of the isomorphism relations on the classes, the classes seem very similar. Hjorth and Thomas showed that the $\\operatorname{TFAb}_r$ are strictly increasing under Borel reducibility. This is not so for the classes $\\operatorname{FD}_r$. Thomas and Velickovic showed that for suffi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.02488","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.02488/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}