{"paper":{"title":"Low complexity Haar null sets without G_{\\delta} hulls in Z^\\omega","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Don\\'at Nagy","submitted_at":"2016-10-21T11:09:05Z","abstract_excerpt":"We show that for every $2\\le \\xi<\\omega_1$ there exists a Haar null set in $\\mathbb{Z}^\\omega$ that is the difference of two $\\mathbf{\\Pi}^0_\\xi$ sets but not contained in any $\\mathbf{\\Pi}^0_\\xi$ Haar null set. In particular, there exists a Haar null set in $\\mathbb{Z}^\\omega$ that is the difference of two $G_\\delta$ sets but not contained in any $G_\\delta$ Haar null set. This partially answers a question of M. Elekes and Z. Vidny\\'anszky. To prove this, we also prove a theorem which characterizes the Haar null subsets of $\\mathbb{Z}^\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06741","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"}