{"paper":{"title":"Length of an intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Christian Delhomm\\'e, Maurice Pouzet","submitted_at":"2015-09-30T20:45:09Z","abstract_excerpt":"A poset $\\bfp$ is well-partially ordered (WPO) if all its linear extensions are well orders~; the supremum of ordered types of these linear extensions is the {\\em length}, $\\ell(\\bfp)$ of $\\bfp$. We prove that if the vertex set $X$ of $\\bfp$ is infinite, of cardinality $\\kappa$, and the ordering $\\leq$ is the intersection of finitely many partial orderings $\\leq_i$ on $X$, $1\\leq i\\leq n$,\n  then, letting $\\ell(X,\\leq_i)=\\kappa\\multordby q_i+r_i$, with $r_i<\\kappa$, denote the euclidian division by $\\kappa$ (seen as an initial ordinal) of the length of the corresponding poset~:\\[ \\ell(\\bfp)< \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00596","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"}