{"paper":{"title":"A Lower Bound for Generalized Dominating Numbers","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dan Hathaway","submitted_at":"2014-01-30T18:31:26Z","abstract_excerpt":"We show a new proof for the fact that when $\\kappa$ and $\\lambda$ are infinite cardinals satisfying $\\lambda ^ \\kappa = \\lambda$, the cofinality of the set of all functions from $\\lambda$ to $\\kappa$ ordered by everywhere domination is $2^\\lambda$. An earlier proof was a consequence of a result about independent families of functions. The new proof follows directly from the main theorem we present: for every $A \\subseteq \\lambda$ there is a function $f: {^\\kappa \\lambda} \\to \\kappa$ such that whenever $M$ is a transitive model of $\\textrm{ZF}$ such that ${^\\kappa \\lambda} \\subseteq M$ and some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7948","kind":"arxiv","version":3},"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"}