{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZPJXUZOSL6XT4FVO6OT57BNM5P","short_pith_number":"pith:ZPJXUZOS","schema_version":"1.0","canonical_sha256":"cbd37a65d25faf3e16aef3a7df85acebd61960279944e31ef62d6353dd992094","source":{"kind":"arxiv","id":"1712.02880","version":5},"attestation_state":"computed","paper":{"title":"Universal classes near $\\aleph_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Marcos Mazari-Armida, Sebastien Vasey","submitted_at":"2017-12-07T22:47:50Z","abstract_excerpt":"Shelah has provided sufficient conditions for an $L_{\\omega_1, \\omega}$-sentence $\\psi$ to have arbitrarily large models and for a Morley-like theorem to hold of $\\psi$. These conditions involve structural and set-theoretic assumptions on all the $\\aleph_n$'s. Using tools of Boney, Shelah, and the second author, we give assumptions on $\\aleph_0$ and $\\aleph_1$ which suffice when $\\psi$ is restricted to be universal:\n  $\\mathbf{Theorem}$ Assume $2^{\\aleph_{0}} < 2 ^{\\aleph_{1}}$. Let $\\psi$ be a universal $L_{\\omega_{1}, \\omega}$-sentence.\n  - If $\\psi$ is categorical in $\\aleph_{0}$ and $1 \\le"},"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":"1712.02880","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-12-07T22:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"52cc2b2b09caa29625b84057b8da9947b2ad4ae01cb67df64640893a96677ae9","abstract_canon_sha256":"6c4b7fa848664da35c5a0e8ea36711ee2efc1c09882d00f6d247584af17e5731"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:38.893469Z","signature_b64":"4M3yhBvadQv6iWu1oVbNYA7Z83Ub7Du9FdcmO7zJzstHi71sXkY9D9woUU1My1BFCtnxsIGrklmw3z+tSIQECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbd37a65d25faf3e16aef3a7df85acebd61960279944e31ef62d6353dd992094","last_reissued_at":"2026-05-17T23:55:38.893065Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:38.893065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal classes near $\\aleph_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Marcos Mazari-Armida, Sebastien Vasey","submitted_at":"2017-12-07T22:47:50Z","abstract_excerpt":"Shelah has provided sufficient conditions for an $L_{\\omega_1, \\omega}$-sentence $\\psi$ to have arbitrarily large models and for a Morley-like theorem to hold of $\\psi$. These conditions involve structural and set-theoretic assumptions on all the $\\aleph_n$'s. Using tools of Boney, Shelah, and the second author, we give assumptions on $\\aleph_0$ and $\\aleph_1$ which suffice when $\\psi$ is restricted to be universal:\n  $\\mathbf{Theorem}$ Assume $2^{\\aleph_{0}} < 2 ^{\\aleph_{1}}$. Let $\\psi$ be a universal $L_{\\omega_{1}, \\omega}$-sentence.\n  - If $\\psi$ is categorical in $\\aleph_{0}$ and $1 \\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02880","kind":"arxiv","version":5},"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":"1712.02880","created_at":"2026-05-17T23:55:38.893135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.02880v5","created_at":"2026-05-17T23:55:38.893135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02880","created_at":"2026-05-17T23:55:38.893135+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPJXUZOSL6XT","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPJXUZOSL6XT4FVO","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPJXUZOS","created_at":"2026-05-18T12:31:59.375834+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/ZPJXUZOSL6XT4FVO6OT57BNM5P","json":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P.json","graph_json":"https://pith.science/api/pith-number/ZPJXUZOSL6XT4FVO6OT57BNM5P/graph.json","events_json":"https://pith.science/api/pith-number/ZPJXUZOSL6XT4FVO6OT57BNM5P/events.json","paper":"https://pith.science/paper/ZPJXUZOS"},"agent_actions":{"view_html":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P","download_json":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P.json","view_paper":"https://pith.science/paper/ZPJXUZOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.02880&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPJXUZOSL6XT4FVO6OT57BNM5P/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPJXUZOSL6XT4FVO6OT57BNM5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P/action/storage_attestation","attest_author":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P/action/author_attestation","sign_citation":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P/action/citation_signature","submit_replication":"https://pith.science/pith/ZPJXUZOSL6XT4FVO6OT57BNM5P/action/replication_record"}},"created_at":"2026-05-17T23:55:38.893135+00:00","updated_at":"2026-05-17T23:55:38.893135+00:00"}