{"paper":{"title":"Can we assign the Borel hulls in a monotone way?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CA","authors_text":"Andr\\'as M\\'ath\\'e, M\\'arton Elekes","submitted_at":"2011-09-22T16:06:29Z","abstract_excerpt":"A \\emph{hull} of $A \\subset [0,1]$ is a set $H$ containing $A$ such that $\\lambda^*(H)=\\lambda^*(A)$. We investigate all four versions of the following problem. Does there exist a monotone (wrt. inclusion) map that assigns a Borel/$G_\\delta$ hull to every negligible/measurable subset of $[0,1]$?\n  Three versions turn out to be independent of ZFC (the usual Zermelo-Fraenkel axioms with the Axiom of Choice), while in the fourth case we only prove that the nonexistence of a monotone $G_\\delta$ hull operation for all measurable sets is consistent. It remains open whether existence here is also con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4862","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"}