{"paper":{"title":"Degrees of Categoricity Above Limit Ordinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barbara F. Csima, Matthew Harrison-Trainor, Michael Deveau, Mohammad Assem Mahmoud","submitted_at":"2018-05-25T17:02:27Z","abstract_excerpt":"A computable structure $\\mathcal{A}$ has degree of categoricity $\\mathbf{d}$ if $\\mathbf{d}$ is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of $\\mathcal{A}$. Fokina, Kalimullin, and Miller showed that every degree d.c.e. in and above $\\mathbf{0}^{(n)}$, for any $n < \\omega$, and also the degree $\\mathbf{0}^{(\\omega)}$, are degrees of categoricity. Later, Csima, Franklin, and Shore showed that every degree $\\mathbf{0}^{(\\alpha)}$ for any computable ordinal $\\alpha$, and every degree d.c.e. in and above $\\mathbf{0}^{(\\alpha)}$ for any successor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10249","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":""},"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"}