{"paper":{"title":"Characterizing large cardinals in terms of layered posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Philipp L\\\"ucke, Sean Cox","submitted_at":"2015-08-16T14:54:47Z","abstract_excerpt":"Given an uncountable regular cardinal $\\kappa$, a partial order is $\\kappa$-stationarily layered if the collection of regular suborders of $\\mathbb{P}$ of cardinality less than $\\kappa$ is stationary in $\\mathcal{P}_\\kappa(\\mathbb{P})$. We show that weak compactness can be characterized by this property of partial orders by proving that an uncountable regular cardinal $\\kappa$ is weakly compact if and only if every partial order satisfying the $\\kappa$-chain condition is $\\kappa$-stationarily layered. We prove a similar result for strongly inaccessible cardinals. Moreover, we show that the sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03831","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"}