{"paper":{"title":"Less than $2^{\\omega}$ many translates of a compact nullset may cover the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.LO","authors_text":"Juris Stepr\\=ans, M\\'arton Elekes","submitted_at":"2011-09-24T20:58:11Z","abstract_excerpt":"We answer a question of Darji and Keleti by proving that there exists a compact set $C_0\\subset\\RR$ of measure zero such that for every perfect set $P\\subset\\RR$ there exists $x\\in\\RR$ such that $(C_0+x)\\cap P$ is uncountable. Using this $C_0$ we answer a question of Gruenhage by showing that it is consistent with $ZFC$ (as it follows e.g. from $\\textrm{cof}(\\iN)<2^\\omega$) that less than $2^\\omega$ many translates of a compact set of measure zero can cover $\\RR$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5307","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"}