{"paper":{"title":"Knaster and friends I: Closed colorings and precalibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Assaf Rinot, Chris Lambie-Hanson","submitted_at":"2018-09-22T19:50:02Z","abstract_excerpt":"The productivity of the $\\kappa$-chain condition, where $\\kappa$ is a regular, uncountable cardinal, has been the focus of a great deal of set-theoretic research. In the 1970s, consistent examples of $\\kappa$-cc posets whose squares are not $\\kappa$-cc were constructed by Laver, Galvin, Roitman and Fleissner. Later, $\\mathsf{ZFC}$ examples were constructed by Todorcevic, Shelah, and others. The most difficult case, that in which $\\kappa = \\aleph_2$, was resolved by Shelah in 1997.\n  In this work, we obtain analogous results regarding the infinite productivity of strong chain conditions, such a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08480","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"}