{"paper":{"title":"The Hurewicz dichotomy for generalized Baire spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luca Motto Ros, Philipp Luecke, Philipp Schlicht","submitted_at":"2015-06-10T15:35:10Z","abstract_excerpt":"By classical results of Hurewicz, Kechris and Saint-Raymond, an analytic subset of a Polish space $X$ is covered by a $K_\\sigma$ subset of $X$ if and only if it does not contain a closed-in-$X$ subset homeomorphic to the Baire space ${}^\\omega \\omega$. We consider the analogous statement (which we call Hurewicz dichotomy) for $\\Sigma^1_1$ subsets of the generalized Baire space ${}^\\kappa \\kappa$ for a given uncountable cardinal $\\kappa$ with $\\kappa=\\kappa^{<\\kappa}$, and show how to force it to be true in a cardinal and cofinality preserving extension of the ground model. Moreover, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03364","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"}