{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:STSO7AZYDY47M5ME5KPHBUJHFG","short_pith_number":"pith:STSO7AZY","schema_version":"1.0","canonical_sha256":"94e4ef83381e39f67584ea9e70d127298b41389aa7777c810fd55d82c0dbcc27","source":{"kind":"arxiv","id":"1201.1725","version":1},"attestation_state":"computed","paper":{"title":"Thin ultrafilters, P-hierarchu and MArtin Axiom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrzej Starosolski, Micha{\\l} Machura","submitted_at":"2012-01-09T10:19:48Z","abstract_excerpt":"Under MA we prove that for the ideal $\\cal I$ of thin sets on $\\omega$ and for any ordinal $\\gamma \\leq \\omega_1$ there is an ${\\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\\cal P}_{\\gamma}$ of P-hierarchy of ultrafilters. Since the class of ${\\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Fla\\v{s}kov\\'a, which states that there are ${\\cal I}$-ultrafilters which are not P-points. It is also related to theorem which states that under CH for any tall P-ideal $\\cal I$ on $\\omega$ there is an ${\\cal I}$-ultrafilter, "},"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":"1201.1725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-09T10:19:48Z","cross_cats_sorted":[],"title_canon_sha256":"ecb21d4560c101a7f3dae3c806b2bc3cfd03a277962c691436f5e9962ecc49cd","abstract_canon_sha256":"4b5816229e630a4b1c291998bd3cd4da5223312b6e99d928fc92494c2eee97e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.838830Z","signature_b64":"798H3ow3jOPRmK0XqmDnzZkvw8AisoAXDzSpRnkcls/yeKr6oghOjFJGevDnQluDKdf79TquWjP3QzNCe52OBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e4ef83381e39f67584ea9e70d127298b41389aa7777c810fd55d82c0dbcc27","last_reissued_at":"2026-05-18T04:04:55.838380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.838380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thin ultrafilters, P-hierarchu and MArtin Axiom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrzej Starosolski, Micha{\\l} Machura","submitted_at":"2012-01-09T10:19:48Z","abstract_excerpt":"Under MA we prove that for the ideal $\\cal I$ of thin sets on $\\omega$ and for any ordinal $\\gamma \\leq \\omega_1$ there is an ${\\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\\cal P}_{\\gamma}$ of P-hierarchy of ultrafilters. Since the class of ${\\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Fla\\v{s}kov\\'a, which states that there are ${\\cal I}$-ultrafilters which are not P-points. It is also related to theorem which states that under CH for any tall P-ideal $\\cal I$ on $\\omega$ there is an ${\\cal I}$-ultrafilter, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1725","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":"1201.1725","created_at":"2026-05-18T04:04:55.838449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1725v1","created_at":"2026-05-18T04:04:55.838449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1725","created_at":"2026-05-18T04:04:55.838449+00:00"},{"alias_kind":"pith_short_12","alias_value":"STSO7AZYDY47","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"STSO7AZYDY47M5ME","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"STSO7AZY","created_at":"2026-05-18T12:27:23.164592+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/STSO7AZYDY47M5ME5KPHBUJHFG","json":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG.json","graph_json":"https://pith.science/api/pith-number/STSO7AZYDY47M5ME5KPHBUJHFG/graph.json","events_json":"https://pith.science/api/pith-number/STSO7AZYDY47M5ME5KPHBUJHFG/events.json","paper":"https://pith.science/paper/STSO7AZY"},"agent_actions":{"view_html":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG","download_json":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG.json","view_paper":"https://pith.science/paper/STSO7AZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1725&json=true","fetch_graph":"https://pith.science/api/pith-number/STSO7AZYDY47M5ME5KPHBUJHFG/graph.json","fetch_events":"https://pith.science/api/pith-number/STSO7AZYDY47M5ME5KPHBUJHFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG/action/storage_attestation","attest_author":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG/action/author_attestation","sign_citation":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG/action/citation_signature","submit_replication":"https://pith.science/pith/STSO7AZYDY47M5ME5KPHBUJHFG/action/replication_record"}},"created_at":"2026-05-18T04:04:55.838449+00:00","updated_at":"2026-05-18T04:04:55.838449+00:00"}