{"paper":{"title":"Games and Ramsey-like cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dan Saattrup Nielsen, Philip Welch","submitted_at":"2018-04-27T08:21:50Z","abstract_excerpt":"We generalise the $\\alpha$-Ramsey cardinals introduced in Holy and Schlicht (2018) for cardinals $\\alpha$ to arbitrary ordinals $\\alpha$, and answer several questions posed in that paper. In particular, we show that $\\alpha$-Ramseys are downwards absolute to the core model $K$ for all $\\alpha$ of uncountable cofinality, that strategic $\\omega$-Ramsey cardinals are equiconsistent with remarkable cardinals and that strategic $\\alpha$-Ramsey cardinals are equiconsistent with measurable cardinals for all $\\alpha>\\omega$. We also show that the $n$-Ramseys satisfy indescribability properties and use"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10383","kind":"arxiv","version":3},"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"}