{"paper":{"title":"On forcing projective generic absoluteness from strong cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Trevor M. Wilson","submitted_at":"2018-07-06T00:29:12Z","abstract_excerpt":"W.H. Woodin showed that if $\\kappa_1 < \\cdots < \\kappa_n$ are strong cardinals then two-step ${\\bf\\Sigma}^1_{n+3}$ generic absoluteness holds after collapsing $2^{2^{\\kappa_n}}$ to be countable. We show that this number can be reduced to $2^{\\kappa_n}$, and to $\\kappa_n^+$ in the case $n = 1$, but cannot be further reduced to $\\kappa_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02206","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"}