{"paper":{"title":"On the equivalence between MV-algebras and $l$-groups with strong unit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Eduardo J. Dubuc, Yuri A. Poveda","submitted_at":"2014-08-05T19:05:31Z","abstract_excerpt":"In \"A new proof of the completeness of the Lukasiewicz axioms\"} (Transactions of the American Mathematical Society, 88) C.C. Chang proved that any totally ordered $MV$-algebra $A$ was isomorphic to the segment $A \\cong \\Gamma(A^*, u)$ of a totally ordered $l$-group with strong unit $A^*$. This was done by the simple intuitive idea of putting denumerable copies of $A$ on top of each other (indexed by the integers). Moreover, he also show that any such group $G$ can be recovered from its segment since $G \\cong \\Gamma(G, u)^*$, establishing an equivalence of categories. In \"Interpretation of AF $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1070","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"}