{"paper":{"title":"Distinguishing perfect set properties in separable metrizable spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Andrea Medini","submitted_at":"2014-05-01T15:32:53Z","abstract_excerpt":"All spaces are assumed to be separable and metrizable. Our main result is that the statement \"For every space $X$, every closed subset of $X$ has the perfect set property if and only if every analytic subset of $X$ has the perfect set property\" is equivalent to $\\mathfrak{b}>\\omega_1$ (hence, in particular, it is independent of $\\mathsf{ZFC}$). This, together with a theorem of Solecki and an example of Miller, will allow us to determine the status of the statement \"For every space $X$, if every $\\mathbf{\\Gamma}$ subset of $X$ has the perfect set property then every $\\mathbf{\\Gamma}'$ subset of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0191","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"}