{"paper":{"title":"Convex choice, finite choice and sorting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Arno Pauly, Takayuki Kihara","submitted_at":"2019-05-02T03:27:00Z","abstract_excerpt":"We study the Weihrauch degrees of closed choice for finite sets, closed choice for convex sets and sorting infinite sequences over finite alphabets. Our main results are: One, that choice for finite sets of cardinality $i + 1$ is reducible to choice for convex sets in dimension $j$, which in turn is reducible to sorting infinite sequences over an alphabet of size $k + 1$, iff $i \\leq j \\leq k$. Two, that convex choice in dimension two is not reducible to the product of convex choice in dimension one with itself. Three, that sequential composition of one-dimensional convex choice is not reducib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03190","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"}