{"paper":{"title":"Generically Computable Linear Orderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Gonzalez, Douglas Cenzer, Valentina Harizanov, Wesley Calvert","submitted_at":"2024-01-26T02:08:51Z","abstract_excerpt":"We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\\Sigma_\\beta$ hierarchy. We focus on linear orderings. We show that at the $\\Sigma_1$ level all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the $\\Sigma_{\\alpha+2}$ level for any $\\alpha\\in\\omega_1^{ck}$ the set of linear orderings with generically or coarsely computable copies is $\\mathbf{\\Sigma}_1^1$-complete and therefore maximally complicated. This development is new "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14598","kind":"arxiv","version":1},"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/2401.14598/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"}