{"paper":{"title":"Square principles in Pmax extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andr\\'es Eduardo Caicedo, Grigor Sargsyan, John Steel, Martin Zeman, Paul Larson, Ralf Schindler","submitted_at":"2012-05-18T22:22:05Z","abstract_excerpt":"By forcing with $\\mathbb{P}_{\\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\\omega_2$ and $\\omega_3$ fail. In particular, we obtain a model of $2^{\\aleph_0}=2^{\\aleph_1}=\\aleph_2 + \\lnot\\square(\\omega_2) + \\lnot\\square(\\omega_3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4275","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"}