{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:S6UG4LIEZRHPCU4UBEKZC3OOV7","short_pith_number":"pith:S6UG4LIE","schema_version":"1.0","canonical_sha256":"97a86e2d04cc4ef153940915916dceafe83a16269c92f32c5ab12ba4f6b5de2a","source":{"kind":"arxiv","id":"1707.06702","version":1},"attestation_state":"computed","paper":{"title":"Boolean ultrapowers, the Bukovsky-Dehornoy phenomenon, and iterated ultrapowers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gunter Fuchs, Joel David Hamkins","submitted_at":"2017-07-20T20:42:41Z","abstract_excerpt":"We show that while the length $\\omega$ iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Prikry forcing, it is consistent that no iteration of length greater than $\\omega$ (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a generalization of Prikry forcing as examples. We refer to the discovery that the intersection of the finite iterates of the universe by a normal measure is the same as the generic extension of the"},"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":"1707.06702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-07-20T20:42:41Z","cross_cats_sorted":[],"title_canon_sha256":"25a4965c48836a40e3c81e093e489cf0b7bf723b46f249cfa2fbb3ae9f4d03aa","abstract_canon_sha256":"2930dc35590577ccc99af3c1f6e5553f37eb60056c815ec0690c158a79803064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.901096Z","signature_b64":"q+dCwcJuF5NmAG78sNpUzRupcg5p/T570oAM07N1kshvavBi517RxTBio4vFBvYhfjfYo4pR1ELiO/u6hKOYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97a86e2d04cc4ef153940915916dceafe83a16269c92f32c5ab12ba4f6b5de2a","last_reissued_at":"2026-05-18T00:39:51.900415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.900415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boolean ultrapowers, the Bukovsky-Dehornoy phenomenon, and iterated ultrapowers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gunter Fuchs, Joel David Hamkins","submitted_at":"2017-07-20T20:42:41Z","abstract_excerpt":"We show that while the length $\\omega$ iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Prikry forcing, it is consistent that no iteration of length greater than $\\omega$ (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a generalization of Prikry forcing as examples. We refer to the discovery that the intersection of the finite iterates of the universe by a normal measure is the same as the generic extension of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06702","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":"1707.06702","created_at":"2026-05-18T00:39:51.900526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06702v1","created_at":"2026-05-18T00:39:51.900526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06702","created_at":"2026-05-18T00:39:51.900526+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6UG4LIEZRHP","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6UG4LIEZRHPCU4U","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6UG4LIE","created_at":"2026-05-18T12:31:43.269735+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/S6UG4LIEZRHPCU4UBEKZC3OOV7","json":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7.json","graph_json":"https://pith.science/api/pith-number/S6UG4LIEZRHPCU4UBEKZC3OOV7/graph.json","events_json":"https://pith.science/api/pith-number/S6UG4LIEZRHPCU4UBEKZC3OOV7/events.json","paper":"https://pith.science/paper/S6UG4LIE"},"agent_actions":{"view_html":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7","download_json":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7.json","view_paper":"https://pith.science/paper/S6UG4LIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06702&json=true","fetch_graph":"https://pith.science/api/pith-number/S6UG4LIEZRHPCU4UBEKZC3OOV7/graph.json","fetch_events":"https://pith.science/api/pith-number/S6UG4LIEZRHPCU4UBEKZC3OOV7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7/action/storage_attestation","attest_author":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7/action/author_attestation","sign_citation":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7/action/citation_signature","submit_replication":"https://pith.science/pith/S6UG4LIEZRHPCU4UBEKZC3OOV7/action/replication_record"}},"created_at":"2026-05-18T00:39:51.900526+00:00","updated_at":"2026-05-18T00:39:51.900526+00:00"}