{"paper":{"title":"Decisive creatures and large continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jakob Kellner, Saharon Shelah","submitted_at":"2006-01-04T22:15:06Z","abstract_excerpt":"For $f,g\\in\\omega\\ho$ let $\\mycfa_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e. for every branch $\\nu$ of the $f$-tree, one of the $g$-trees contains $\\nu$. $\\myc_{f,g}$ is the dual notion: For every branch $\\nu$, one of the $g$-trees guesses $\\nu(m)$ infinitely often.\n  It is consistent that $\\myc_{f_\\epsilon,g_\\epsilon}=\\mycfa_{f_\\epsilon,g_\\epsilon}=\\kappa_\\epsilon$ for $\\al1$ many pairwise different cardinals $\\kappa_\\epsilon$ and suitable pairs $(f_\\epsilon,g_\\epsilon)$.\n  For the proof we use creatures with sufficient big"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601083","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"}