{"paper":{"title":"States on EMV-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Anatolij Dvure\\v{c}enskij, Omid Zahiri","submitted_at":"2017-08-21T06:50:17Z","abstract_excerpt":"We define a state as a $[0,1]$-valued, finitely additive function attaining the value $1$ on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. We show that states always exist, the extremal states are exactly state-morphisms. Nevertheless the state space is a convex space that is not necessarily compact, a variant of the Krein--Mil'man theorem saying states are generated by extremal states, is proved. We define a weaker form of states, pre-states and strong pre-states, and also Jordan signed measures which form a Dedekind complete $\\ell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06091","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"}