{"paper":{"title":"Poset algebras over well quasi-ordered posets","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Robert Bonnet, Uri Abraham, Wieslaw Kubis","submitted_at":"2007-02-20T17:37:50Z","abstract_excerpt":"A new class of partial order-types, class $\\gbqo^+$ is defined and investigated here. A poset $P$ is in the class $W^+ $ iff the free poset algebra $F(P)$ is generated by a better quasi-order $G$ that is included in the free lattice $L(P)$.\n  We prove that if $P$ is any well quasi-ordering, then $L(P)$ is well founded, and is a countable union of well quasi-orderings. We prove that the class $W^+$ is contained in the class of well quasi-ordered sets. We prove that $W^+$ is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702585","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"}