{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:45DQELOEMXFEF6B5W6ZC7XER5E","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f0e38b704e281615ddaef7ba7dda6fc58dfe1ef2cc3221d42e4432977714d4e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-02T20:30:03Z","title_canon_sha256":"31db20148b946dbadcab4120ac651fd17e49d12bae8b4e5d19244ae4cd30c9f0"},"schema_version":"1.0","source":{"id":"1211.0558","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0558","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0558v3","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0558","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"45DQELOEMXFE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"45DQELOEMXFEF6B5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"45DQELOE","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:07662e0db4ba21199eab30cafb85adb1ffb51a101babef82c6d115b815ab1307","target":"graph","created_at":"2026-05-18T02:50:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study aleph_0-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of lambda-Borel completeness and prove that such theories are lambda-Borel complete. Using this, we conclude that an aleph_0-stable theory has 2^lambda pairwise non-L(infinity,aleph_0) equivalent models of size lambda for all infinite cardinals lambda if and only if T either has eni-DOP or is eni-deep.","authors_text":"Michael C. Laskowski, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-02T20:30:03Z","title":"Borel completeness of some aleph_0 stable theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0558","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:90e028c6177bdb92cc87a6ab87c908bdfa78f5f4d891dea53fd3da5b3bff534b","target":"record","created_at":"2026-05-18T02:50:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f0e38b704e281615ddaef7ba7dda6fc58dfe1ef2cc3221d42e4432977714d4e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-02T20:30:03Z","title_canon_sha256":"31db20148b946dbadcab4120ac651fd17e49d12bae8b4e5d19244ae4cd30c9f0"},"schema_version":"1.0","source":{"id":"1211.0558","kind":"arxiv","version":3}},"canonical_sha256":"e747022dc465ca42f83db7b22fdc91e9136f1a56d46b53ee2b44f505d97ffa3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e747022dc465ca42f83db7b22fdc91e9136f1a56d46b53ee2b44f505d97ffa3b","first_computed_at":"2026-05-18T02:50:32.592539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:32.592539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gjGKbbV5iqRMND0hN8xfdbuyOKB507iI6leN++1XqMjgoqvPYIJCoSRvktSKXpkNpR83lCiABI5tHYrcQKZbAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:32.593008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0558","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e028c6177bdb92cc87a6ab87c908bdfa78f5f4d891dea53fd3da5b3bff534b","sha256:07662e0db4ba21199eab30cafb85adb1ffb51a101babef82c6d115b815ab1307"],"state_sha256":"0112601b493b154b97e3217aaf0c17652703ba250502b09cfa37374ba5dfb1bf"}