{"paper":{"title":"Amenable colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Shimon Garti","submitted_at":"2016-11-06T10:56:29Z","abstract_excerpt":"Let $\\kappa$ be any regular cardinal. Assuming the existence of a huge cardinal above $\\kappa$, we prove the consistency of $\\binom{\\kappa^{++}}{\\kappa^+}\\rightarrow\\binom{\\tau}{\\kappa^+}$ for every ordinal $\\tau<\\kappa^{++}$. Likewise, we prove a full amenable relation for $(\\aleph_2,\\aleph_1)$ with respect to collections which are strongly closed under countable intersections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01756","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"}