{"paper":{"title":"The consistency strength of the perfect set property for universally Baire sets of reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ralf Schindler, Trevor M. Wilson","submitted_at":"2018-07-06T01:17:29Z","abstract_excerpt":"We show that the statement \"every universally Baire set of reals has the perfect set property\" is equiconsistent modulo ZFC with the existence of a cardinal that we call a virtually Shelah cardinal. These cardinals resemble Shelah cardinals but are much weaker: if $0^\\sharp$ exists then every Silver indiscernible is virtually Shelah in $L$. We also show that the statement $\\text{uB} = {\\bf\\Delta}^1_2$, where $\\text{uB}$ is the pointclass of all universally Baire sets of reals, is equiconsistent modulo ZFC with the existence of a $\\Sigma_2$-reflecting virtually Shelah cardinal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02213","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"}