{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZRFKOISV47YMUA7BMP4CKRCZZF","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":"195e68d34b0353a8cbfb75fcc273783cd5e8bb82be28c42074ac0075483523e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-03-06T19:49:44Z","title_canon_sha256":"a06492d54786d98ba7243c99846f1291927b67bf99e0c45594d55083ff840114"},"schema_version":"1.0","source":{"id":"1703.02082","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02082","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02082v2","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02082","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZRFKOISV47YM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZRFKOISV47YMUA7B","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZRFKOISV","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:af3b32b5a5bbd16bf5f8de660178adb89809c3fe5cb233bc4f5af2f7f7d327fb","target":"graph","created_at":"2026-05-18T00:02:22Z","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 prove that after adding a Silver real no ultrafilter from the ground model can be extended to a P-point, and this remains to be the case in any further extension which has the Sacks property. We conclude that there are no P-points in the Silver model. In particular, it is possible to construct a model without P-points by iterating Borel partial orders. This answers a question of Michael Hru\\v{s}\\'ak. We also show that the same argument can be used for the side-by-side product of Silver forcing. This provides a model without P-points with the continuum arbitrary large, answering a question o","authors_text":"David Chodounsk\\'y, Osvaldo Guzm\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-03-06T19:49:44Z","title":"There are no P-points in Silver extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02082","kind":"arxiv","version":2},"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:fe6d1434811e622b3186e5e74c596b9840bf01ea749d399af3faf41387ae5949","target":"record","created_at":"2026-05-18T00:02:22Z","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":"195e68d34b0353a8cbfb75fcc273783cd5e8bb82be28c42074ac0075483523e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-03-06T19:49:44Z","title_canon_sha256":"a06492d54786d98ba7243c99846f1291927b67bf99e0c45594d55083ff840114"},"schema_version":"1.0","source":{"id":"1703.02082","kind":"arxiv","version":2}},"canonical_sha256":"cc4aa72255e7f0ca03e163f8254459c97c77052f610399d2702c226445867a33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc4aa72255e7f0ca03e163f8254459c97c77052f610399d2702c226445867a33","first_computed_at":"2026-05-18T00:02:22.627273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:22.627273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qO6i1eMuwOZFSBmKDFAfJlsOuUVwyCWDb6j0XLK1fT/6SIXSz6hDgoCE5kNd2DG+sh0fDMah6AUZhWyJCNDJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:22.627915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02082","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe6d1434811e622b3186e5e74c596b9840bf01ea749d399af3faf41387ae5949","sha256:af3b32b5a5bbd16bf5f8de660178adb89809c3fe5cb233bc4f5af2f7f7d327fb"],"state_sha256":"4b562ff393be4ae34fd961303d3b7ccbdd264417befb15939df4be57c702b7d1"}