{"paper":{"title":"Characterizing the strongly jump-traceable sets via randomness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andre Nies, Denis Hirschfeldt, Noam Greenberg","submitted_at":"2011-09-30T08:34:31Z","abstract_excerpt":"We show that if a set $A$ is computable from every superlow 1-random set, then $A$ is strongly jump-traceable. This theorem shows that the computably enumerable (c.e.) strongly jump-traceable sets are exactly the c.e.\\ sets computable from every superlow 1-random set.\n  We also prove the analogous result for superhighness: a c.e.\\ set is strongly jump-traceable if and only if it is computable from every superhigh 1-random set.\n  Finally, we show that for each cost function $c$ with the limit condition there is a 1-random $\\Delta^0_2$ set $Y$ such that every c.e.\\ set $A \\le_T Y$ obeys $c$. To "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6749","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":""},"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"}