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As a corollary we deduce that two such reduced products $\\prod A_n / \\bigoplus A_n$ and $\\prod B_n / \\bigoplus B_n$ are isomorphic if and only if, up to an almost-permutation of $\\mathbb{N}$, $A_n$ is isomorphic to $B_n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.5037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-03-20T19:29:49Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"7a78235e2ba9d0356c1bde315549b73288ef756e51e9abc8571ec76388724f51","abstract_canon_sha256":"d86c2d8150e1d67a79aa5b6451168b8acd51116745e1087ae627d2d03e815038"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:15.259651Z","signature_b64":"a9Hd/vtJxZYYIw2U6xrnh8xg+lFxdsbPX95W5e07UNSNsgaJuTO5Q73WCEV1wcJKpBGbNbvLKablBJdv/q3ODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45693dd0907ad43f9104c57a7c0c90c36ee5e150a36aa5365b753dee130a197f","last_reissued_at":"2026-05-18T03:30:15.258456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:15.258456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduced products of UHF algebras under forcing axioms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.LO","authors_text":"Paul McKenney","submitted_at":"2013-03-20T19:29:49Z","abstract_excerpt":"If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\\prod A_n / \\bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic's Axiom and Martin's Axiom, that every isomorphism between two reduced products of separable, unital UHF algebras must be definable in a strong sense. As a corollary we deduce that two such reduced products $\\prod A_n / \\bigoplus A_n$ and $\\prod B_n / \\bigoplus B_n$ are isomorphic if and only if, up to an almost-permutation of $\\mathbb{N}$, $A_n$ is isomorphic to $B_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5037","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.5037","created_at":"2026-05-18T03:30:15.258659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5037v1","created_at":"2026-05-18T03:30:15.258659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5037","created_at":"2026-05-18T03:30:15.258659+00:00"},{"alias_kind":"pith_short_12","alias_value":"IVUT3UEQPLKD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"IVUT3UEQPLKD7EIE","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"IVUT3UEQ","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN","json":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN.json","graph_json":"https://pith.science/api/pith-number/IVUT3UEQPLKD7EIEYV5HYDEQYN/graph.json","events_json":"https://pith.science/api/pith-number/IVUT3UEQPLKD7EIEYV5HYDEQYN/events.json","paper":"https://pith.science/paper/IVUT3UEQ"},"agent_actions":{"view_html":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN","download_json":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN.json","view_paper":"https://pith.science/paper/IVUT3UEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5037&json=true","fetch_graph":"https://pith.science/api/pith-number/IVUT3UEQPLKD7EIEYV5HYDEQYN/graph.json","fetch_events":"https://pith.science/api/pith-number/IVUT3UEQPLKD7EIEYV5HYDEQYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN/action/storage_attestation","attest_author":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN/action/author_attestation","sign_citation":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN/action/citation_signature","submit_replication":"https://pith.science/pith/IVUT3UEQPLKD7EIEYV5HYDEQYN/action/replication_record"}},"created_at":"2026-05-18T03:30:15.258659+00:00","updated_at":"2026-05-18T03:30:15.258659+00:00"}