{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AYTXLGRU4KTVLVEHAEDDFG3D26","short_pith_number":"pith:AYTXLGRU","schema_version":"1.0","canonical_sha256":"0627759a34e2a755d4870106329b63d79a8c964fe9c038a392676b7f631e31b4","source":{"kind":"arxiv","id":"1208.2579","version":1},"attestation_state":"computed","paper":{"title":"Model-theoretic properties of ultrafilters built by independent families of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"M. Malliaris, S. Shelah","submitted_at":"2012-08-13T13:15:52Z","abstract_excerpt":"Our results in this paper increase the model-theoretic precision of a widely used method for building ultrafilters, and so advance the general problem of constructing ultrafilters whose ultrapowers have a precise degree of saturation. We begin by showing that any flexible regular ultrafilter makes the product of an unbounded sequence of finite cardinals large, {thus} saturating any stable theory. We then prove directly that a \"bottleneck\" in the inductive construction of a regular ultrafilter on $\\lambda$ (i.e. a point after which all antichains of $P(\\lambda)/D$ have cardinality less than $\\l"},"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":"1208.2579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-13T13:15:52Z","cross_cats_sorted":[],"title_canon_sha256":"138100919b8ae1c8183d49c76ea31cb40ce2c79dfd6fa8a0c619390586946535","abstract_canon_sha256":"b8e6675d042801b04e4798a7873e6c3283b3a84275c393e363a99992c93a645e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:57.500040Z","signature_b64":"ZEcKd29ov/8YCuMx7DkthBNAEcrJ2Cc2QVaPakhpYMuQutpoV17OPoNO0HidmpM+ASiyZyYKacJ3OQi8DN2PCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0627759a34e2a755d4870106329b63d79a8c964fe9c038a392676b7f631e31b4","last_reissued_at":"2026-05-18T03:48:57.499253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:57.499253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Model-theoretic properties of ultrafilters built by independent families of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"M. Malliaris, S. Shelah","submitted_at":"2012-08-13T13:15:52Z","abstract_excerpt":"Our results in this paper increase the model-theoretic precision of a widely used method for building ultrafilters, and so advance the general problem of constructing ultrafilters whose ultrapowers have a precise degree of saturation. We begin by showing that any flexible regular ultrafilter makes the product of an unbounded sequence of finite cardinals large, {thus} saturating any stable theory. We then prove directly that a \"bottleneck\" in the inductive construction of a regular ultrafilter on $\\lambda$ (i.e. a point after which all antichains of $P(\\lambda)/D$ have cardinality less than $\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2579","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":"1208.2579","created_at":"2026-05-18T03:48:57.499399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.2579v1","created_at":"2026-05-18T03:48:57.499399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2579","created_at":"2026-05-18T03:48:57.499399+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYTXLGRU4KTV","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYTXLGRU4KTVLVEH","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYTXLGRU","created_at":"2026-05-18T12:26:58.693483+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/AYTXLGRU4KTVLVEHAEDDFG3D26","json":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26.json","graph_json":"https://pith.science/api/pith-number/AYTXLGRU4KTVLVEHAEDDFG3D26/graph.json","events_json":"https://pith.science/api/pith-number/AYTXLGRU4KTVLVEHAEDDFG3D26/events.json","paper":"https://pith.science/paper/AYTXLGRU"},"agent_actions":{"view_html":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26","download_json":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26.json","view_paper":"https://pith.science/paper/AYTXLGRU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.2579&json=true","fetch_graph":"https://pith.science/api/pith-number/AYTXLGRU4KTVLVEHAEDDFG3D26/graph.json","fetch_events":"https://pith.science/api/pith-number/AYTXLGRU4KTVLVEHAEDDFG3D26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26/action/storage_attestation","attest_author":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26/action/author_attestation","sign_citation":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26/action/citation_signature","submit_replication":"https://pith.science/pith/AYTXLGRU4KTVLVEHAEDDFG3D26/action/replication_record"}},"created_at":"2026-05-18T03:48:57.499399+00:00","updated_at":"2026-05-18T03:48:57.499399+00:00"}