{"paper":{"title":"Free monoids and generalized metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ivo Rosenberg, Maurice Pouzet, Mustapha Kabil","submitted_at":"2017-05-27T01:18:39Z","abstract_excerpt":"Let $A$ be an ordered alphabet, $A^{\\ast}$ be the free monoid over $A$ ordered by the Higman ordering, and let $F(A^{\\ast})$ be the set of final segments of $A^{\\ast}$. With the operation of concatenation, this set is a monoid. We show that the submonoid $F^{\\circ}(A^{\\ast}):= F(A^{\\ast})\\setminus \\{\\emptyset\\}$ is free. The MacNeille completion $N(A^{\\ast})$ of $A^{\\ast}$ is a submonoid of $F(A^{\\ast})$. As a corollary, we obtain that the monoid $N^{\\circ}(A^{\\ast}):=N(A^{\\ast})\\setminus \\{\\emptyset\\}$ is free. We give an interpretation of the freeness of $F^{\\circ}(A^{\\ast})$ in the category"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09750","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"}