{"paper":{"title":"On idealized versions of $\\pr_1(\\mu^+,\\mu^+,\\mu^+,\\cf(\\mu))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Todd Eisworth","submitted_at":"2012-10-21T19:58:22Z","abstract_excerpt":"We obtain an improvement of some coloring theorems from \\cite{nsbpr}, \\cite{819}, and \\cite{APAL} for the case where the singular cardinal in question has countable cofinality. As a corollary, we obtain an \"idealized\" version of the combinatorial principle $\\pr_1(\\mu^+,\\mu^+,\\mu^+,\\cf(\\mu))$ that maximizes the indecomposability of the associated ideal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5759","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"}