{"paper":{"title":"Density-1-bounding and quasiminimality in the generic degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gregory Igusa, Peter Cholak","submitted_at":"2015-12-30T18:50:54Z","abstract_excerpt":"We consider the question \"Is every nonzero generic degree a density-1-bounding generic degree?\" By previous results \\cite{I2} either resolution of this question would answer an open question concerning the structure of the generic degrees: A positive result would prove that there are no minimal generic degrees, and a negative result would prove that there exist minimal pairs in the generic degrees.\n  We consider several techniques for showing that the answer might be positive, and use those techniques to prove that a wide class of assumptions is sufficient to prove density-1-bounding.\n  We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09057","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"}