{"paper":{"title":"Ladder system uniformization on trees I & II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2018-06-11T09:10:00Z","abstract_excerpt":"Given a tree $T$ of height $\\omega_1$, we say that a ladder system colouring $(f_\\alpha)_{\\alpha\\in \\lim\\omega_1}$ has a $T$-uniformization if there is a function $\\varphi$ defined on a subtree $S$ of $T$ so that for any $s\\in S_\\alpha$ of limit height and almost all $\\xi\\in {dom} (f_\\alpha)$, $\\varphi(s\\upharpoonright \\xi)=f_\\alpha(\\xi)$. In sharp contrast to the classical theory of uniformizations on $\\omega_1$, J. Moore proved that CH is consistent with the statement that any ladder system colouring has a $T$-uniformization (for any Aronszajn tree $T$). Our goal is to present a fine analysi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03867","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"}