{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4B2HLLPX6OKPGK2OGXDJXERPWB","short_pith_number":"pith:4B2HLLPX","schema_version":"1.0","canonical_sha256":"e07475adf7f394f32b4e35c69b922fb05e2e9e679dd8793274840019dd50731b","source":{"kind":"arxiv","id":"1605.04735","version":1},"attestation_state":"computed","paper":{"title":"Towers in filters, cardinal invariants, and Luzin type families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnab\\'as Farkas, Jonathan Verner, J\\\"org Brendle","submitted_at":"2016-05-16T11:44:00Z","abstract_excerpt":"We investigate which filters on $\\omega$ can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in $[\\omega]^\\omega$). We prove the following results:\n  - Many classical examples of nice tall filters contain no towers (in ZFC).\n  - It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well).\n  - It is consistent that all towers generate non-meager filters, in particular (consistently) Borel filters do not contain towers.\n  - The statement \"Every ultrafilter contains towers"},"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":"1605.04735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-16T11:44:00Z","cross_cats_sorted":[],"title_canon_sha256":"e8a4470c791660c73b233100be330e4b7a24bd489901a146724ddbdf9a8582ec","abstract_canon_sha256":"63128da5238839087ceba74eb0d6490b0a009f6d1b4edf6bb04eb7d9bc2c678b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:46.385655Z","signature_b64":"JSBxRH6MsnOzFj9pY4S7A9Zuz23Bv3p0Q2RGzXTm3whVQ1cLsMpu/vBGfg1DgCYDDTlio1lSb8AP7sWlf84NCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e07475adf7f394f32b4e35c69b922fb05e2e9e679dd8793274840019dd50731b","last_reissued_at":"2026-05-18T01:14:46.385108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:46.385108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towers in filters, cardinal invariants, and Luzin type families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnab\\'as Farkas, Jonathan Verner, J\\\"org Brendle","submitted_at":"2016-05-16T11:44:00Z","abstract_excerpt":"We investigate which filters on $\\omega$ can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in $[\\omega]^\\omega$). We prove the following results:\n  - Many classical examples of nice tall filters contain no towers (in ZFC).\n  - It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well).\n  - It is consistent that all towers generate non-meager filters, in particular (consistently) Borel filters do not contain towers.\n  - The statement \"Every ultrafilter contains towers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04735","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":"1605.04735","created_at":"2026-05-18T01:14:46.385188+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.04735v1","created_at":"2026-05-18T01:14:46.385188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04735","created_at":"2026-05-18T01:14:46.385188+00:00"},{"alias_kind":"pith_short_12","alias_value":"4B2HLLPX6OKP","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4B2HLLPX6OKPGK2O","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4B2HLLPX","created_at":"2026-05-18T12:29:58.707656+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/4B2HLLPX6OKPGK2OGXDJXERPWB","json":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB.json","graph_json":"https://pith.science/api/pith-number/4B2HLLPX6OKPGK2OGXDJXERPWB/graph.json","events_json":"https://pith.science/api/pith-number/4B2HLLPX6OKPGK2OGXDJXERPWB/events.json","paper":"https://pith.science/paper/4B2HLLPX"},"agent_actions":{"view_html":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB","download_json":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB.json","view_paper":"https://pith.science/paper/4B2HLLPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.04735&json=true","fetch_graph":"https://pith.science/api/pith-number/4B2HLLPX6OKPGK2OGXDJXERPWB/graph.json","fetch_events":"https://pith.science/api/pith-number/4B2HLLPX6OKPGK2OGXDJXERPWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB/action/storage_attestation","attest_author":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB/action/author_attestation","sign_citation":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB/action/citation_signature","submit_replication":"https://pith.science/pith/4B2HLLPX6OKPGK2OGXDJXERPWB/action/replication_record"}},"created_at":"2026-05-18T01:14:46.385188+00:00","updated_at":"2026-05-18T01:14:46.385188+00:00"}