{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:37MLOMNORDUJ447X5IG4CAVXD2","short_pith_number":"pith:37MLOMNO","schema_version":"1.0","canonical_sha256":"dfd8b731ae88e89e73f7ea0dc102b71ea36ff1600d6a9e4fae32d45a6cfd2308","source":{"kind":"arxiv","id":"1503.00318","version":1},"attestation_state":"computed","paper":{"title":"Constructing many atomic models in $\\aleph_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jerusalem), John T. Baldwin (U. Ill. Chicago), Michael C. Laskowski (U. of Maryland), Saharon Shelah (Hebrew University","submitted_at":"2015-03-01T17:37:20Z","abstract_excerpt":"We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\\omega_1,\\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are $2^{\\aleph_1}$ pairwise non-isomorphic atomic models of $T$, each of size $\\aleph_1$."},"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":"1503.00318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-01T17:37:20Z","cross_cats_sorted":[],"title_canon_sha256":"d0982313dc6d26948fcb9f2196e66b6b128cc09ba31f2f0896e1a5bf37c52cc3","abstract_canon_sha256":"c2fea23c914b589c26fdf6f485f68d0d10d712d8c63a2a46c29ace9836b18a9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:54.681924Z","signature_b64":"iOWirs5bPoaJReuzv9ED+LxfaBb8ZPy2MlHyDthIWHqA7WX7kEvqTM3JfuqU3ySWJjOEt5p03Od2KuS+QbWfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfd8b731ae88e89e73f7ea0dc102b71ea36ff1600d6a9e4fae32d45a6cfd2308","last_reissued_at":"2026-05-18T02:25:54.681525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:54.681525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing many atomic models in $\\aleph_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jerusalem), John T. Baldwin (U. Ill. Chicago), Michael C. Laskowski (U. of Maryland), Saharon Shelah (Hebrew University","submitted_at":"2015-03-01T17:37:20Z","abstract_excerpt":"We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\\omega_1,\\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are $2^{\\aleph_1}$ pairwise non-isomorphic atomic models of $T$, each of size $\\aleph_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00318","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":"1503.00318","created_at":"2026-05-18T02:25:54.681594+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00318v1","created_at":"2026-05-18T02:25:54.681594+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00318","created_at":"2026-05-18T02:25:54.681594+00:00"},{"alias_kind":"pith_short_12","alias_value":"37MLOMNORDUJ","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"37MLOMNORDUJ447X","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"37MLOMNO","created_at":"2026-05-18T12:29:02.477457+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/37MLOMNORDUJ447X5IG4CAVXD2","json":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2.json","graph_json":"https://pith.science/api/pith-number/37MLOMNORDUJ447X5IG4CAVXD2/graph.json","events_json":"https://pith.science/api/pith-number/37MLOMNORDUJ447X5IG4CAVXD2/events.json","paper":"https://pith.science/paper/37MLOMNO"},"agent_actions":{"view_html":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2","download_json":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2.json","view_paper":"https://pith.science/paper/37MLOMNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00318&json=true","fetch_graph":"https://pith.science/api/pith-number/37MLOMNORDUJ447X5IG4CAVXD2/graph.json","fetch_events":"https://pith.science/api/pith-number/37MLOMNORDUJ447X5IG4CAVXD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2/action/storage_attestation","attest_author":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2/action/author_attestation","sign_citation":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2/action/citation_signature","submit_replication":"https://pith.science/pith/37MLOMNORDUJ447X5IG4CAVXD2/action/replication_record"}},"created_at":"2026-05-18T02:25:54.681594+00:00","updated_at":"2026-05-18T02:25:54.681594+00:00"}