{"paper":{"title":"Pairs of orthogonal countable ordinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claude Laflamme, Imed Zaguia, Maurice Pouzet, Nobert Sauer","submitted_at":"2014-07-03T15:03:06Z","abstract_excerpt":"We characterize pairs of orthogonal countable ordinals. Two ordinals $\\alpha$ and $\\beta$ are orthogonal if there are two linear orders $A$ and $B$ on the same set $V$ with order types $\\alpha$ and $\\beta$ respectively such that the only maps preserving both orders are the constant maps and the identity map. We prove that if $\\alpha$ and $\\beta$ are two countable ordinals, with $\\alpha \\leq \\beta$, then $\\alpha$ and $\\beta$ are orthogonal if and only if either $\\omega + 1\\leq \\alpha$ or $\\alpha =\\omega$ and $\\beta < \\omega \\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0940","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"}