{"paper":{"title":"Partial strong compactness and squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yair Hayut","submitted_at":"2018-04-16T15:58:08Z","abstract_excerpt":"In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\\mathcal{L}_{\\kappa,\\kappa}$. Using this equivalence we show that if any $\\kappa$-complete filter on $\\lambda$ can be extended to a $\\kappa$-complete ultrafilter and $\\lambda^{<\\kappa} = \\lambda$ then $\\square(\\mu)$ fails for all regular $\\mu\\in[\\kappa,2^\\lambda]$. As an application, we improve the lower bound for the consistency strength of $\\kappa$-compactness, a case which was explicitly considered by Mitchell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05758","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"}