{"paper":{"title":"Measurable cardinals and good $\\Sigma_1(\\kappa)$-wellorderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Philipp L\\\"ucke, Philipp Schlicht","submitted_at":"2017-04-03T10:16:18Z","abstract_excerpt":"We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals $\\kappa$ with the property that the collection of all initial segments of the wellordering is definable by a $\\Sigma_1$-formula with parameter $\\kappa$. A short argument shows that the existence of a measurable cardinal $\\delta$ implies that such wellorderings do not exist at $\\delta$-inaccessible cardinals of cofinality not equal to $\\delta$ and their successors. In contrast, our main result shows that these wellorderings exist at all other uncountable cardinals in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00511","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"}