{"paper":{"title":"Weak square and stationary reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Assaf Rinot, Gunter Fuchs","submitted_at":"2017-11-16T17:34:13Z","abstract_excerpt":"It is well-known that the square principle $\\square_\\lambda$ entails the existence of a non-reflecting stationary subset of $\\lambda^+$, whereas the weak square principle $\\square^*_\\lambda$ does not. Here we show that if $\\mu^{\\mathrm{cf}(\\lambda)} < \\lambda$ for all $\\mu < \\lambda$, then $\\square^*_\\lambda$ entails the existence of a non-reflecting stationary subset of $E^{\\lambda^+}_{\\mathrm{cf}(\\lambda)}$ in the forcing extension for adding a single Cohen subset of $\\lambda^+$. It follows that indestructible forms of simultaneous stationary reflection entail the failure of weak square. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06213","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"}