{"paper":{"title":"Arrow type impossibility theorems over median algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Gerasimos C. Meletiou, Miguel Couceiro, Stephan Foldes","submitted_at":"2015-08-19T18:56:33Z","abstract_excerpt":"We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a product $\\mathbf{A}_1\\times \\cdots \\times \\mathbf{A}_n$ of median algebras to a median algebra $\\mathbf{B}$ are possible if and only if $\\mathbf{B}$ is a tree, when thought of as an ordered structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04741","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"}