{"paper":{"title":"Quantum measurable cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OA","authors_text":"David P. Blecher, Nik Weaver","submitted_at":"2016-07-28T15:44:51Z","abstract_excerpt":"We investigate states on von Neumann algebras which are not normal but enjoy various forms of infinite additivity, and show that these exist on $B(H)$ if and only if the cardinality of an orthonormal basis of $H$ satisfies various large cardinal conditions. For instance, there is a singular countably additive pure state on $B(l^2(\\kappa))$ if and only if $\\kappa$ is Ulam measurable, and there is a singular ${<}\\,\\kappa$-additive pure state on $B(l^2(\\kappa))$ if and only if $\\kappa$ is measurable. The proofs make use of Farah and Weaver's theory of quantum filters. Applications to Ueda's peak "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08505","kind":"arxiv","version":2},"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"}