{"paper":{"title":"The weakly compact reflection principle need not imply a high order of weak compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody, Hiroshi Sakai","submitted_at":"2017-07-26T15:43:12Z","abstract_excerpt":"The weakly compact reflection principle $\\text{Refl}_{\\text{wc}}(\\kappa)$ states that $\\kappa$ is a weakly compact cardinal and every weakly compact subset of $\\kappa$ has a weakly compact proper initial segment. The weakly compact reflection principle at $\\kappa$ implies that $\\kappa$ is an $\\omega$-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that $\\kappa$ is $(\\omega+1)$-weakly compact. Moreover, we show that if the weakly compact reflection principle holds at $\\kappa$ then there is a forcing extension preserving this in which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08506","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"}