{"paper":{"title":"Less nonstationary ideals","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Moti Gitik, Saharon Shelah","submitted_at":"1995-03-01T00:00:00Z","abstract_excerpt":"We are proving the following:\n (1) If $\\kap$ is a weakly inaccessible then $NS_\\kap$  is not $\\kap^+$-saturated.\n (2) If $\\kap$  is a weakly inaccessible and $\\tet <\\kap$ is regular then $NS^\\tet_\\kap$  is not $\\kap^+$-saturated.\n (3) If $\\kap$  is singular then $NS^{cf\\kap}_{\\kap^+}$ is not $\\kap^{++}$-saturated.\n  Combining this with previous results of Shelah, one obtains the following:\n (A) If $\\kap >\\aleph_1$  then $NS_\\kap$ is not $\\kap^+$-saturated.\n (B) If $\\tet^+<\\kap$  then $NS^\\tet_\\kap$ is not $\\kap^+$-saturated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9503203","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"}