{"paper":{"title":"The Ostaszewski square, and homogenous Souslin trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Assaf Rinot","submitted_at":"2011-05-15T13:05:01Z","abstract_excerpt":"Assume GCH and let $\\lambda$ denote an uncountable cardinal. We prove that if $\\square_\\lambda$ holds, then this may be witnessed by a coherent sequence $< C_\\alpha | \\alpha < \\lambda^+ >$ with the following remarkable guessing property:\n  For every sequence $< A_i | i<\\lambda >$ of unbounded subsets of $\\lambda^+$, and every limit $\\theta<\\lambda$, there exists some $\\alpha<\\lambda^+$ such that $\\otp(C_\\alpha)=\\theta$, and the $(i+1)_{th}$-element of $C_\\alpha$ is a member of $A_i$, for all $i<\\theta$.\n  As an application, we construct an homogenous $\\lambda^+$-Souslin tree from $GCH+\\square_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2944","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"}