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Assuming the classical Borel conjecture, $\\neg{\\sf BC}_{\\aleph_1}$ is equivalent to the existence of a Kurepa tree of height $\\aleph_1$. Using the connection of ${\\sf BC}_{\\kappa}$ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results:\n  (1)If it is consistent that there is a 1-inaccessible cardinal then it is consistent that ${\\"},"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":"1107.5383","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-07-27T05:05:29Z","cross_cats_sorted":["math.GN","math.GR"],"title_canon_sha256":"3efc90f3f00166d1c4ea1bc6002babe377633ed8054309842e9c9a20367117d1","abstract_canon_sha256":"61825c1012c523b70578f0556a3614ab990367fcc931e65930792f496ad38ab7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:47.304510Z","signature_b64":"LHBO4pk9bI5bfxzJlrE5Dc0K6rYfAgm/hm6THZmPFhwOGnXAHeIUc3OgmRg3bd3vUt8EeKLcudQIkJfW4pf+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e45f1746cd3291e0434422c5758a41243cda37a455c864e98c735653a6b4f1ee","last_reissued_at":"2026-05-18T03:51:47.303827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:47.303827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Borel's Conjecture in Topological Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GR"],"primary_cat":"math.LO","authors_text":"Fred Galvin, Marion Scheepers","submitted_at":"2011-07-27T05:05:29Z","abstract_excerpt":"We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number $\\kappa$, let {\\sf BC}$_{\\kappa}$ denote this generalization. Then ${\\sf BC}_{\\aleph_0}$ is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, $\\neg{\\sf BC}_{\\aleph_1}$ is equivalent to the existence of a Kurepa tree of height $\\aleph_1$. Using the connection of ${\\sf BC}_{\\kappa}$ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results:\n  (1)If it is consistent that there is a 1-inaccessible cardinal then it is consistent that ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5383","kind":"arxiv","version":2},"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":"1107.5383","created_at":"2026-05-18T03:51:47.303937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.5383v2","created_at":"2026-05-18T03:51:47.303937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5383","created_at":"2026-05-18T03:51:47.303937+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RPRORWNGKI6","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RPRORWNGKI6AQ2E","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RPRORWN","created_at":"2026-05-18T12:26:20.644004+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/4RPRORWNGKI6AQ2EELCXLCSBEQ","json":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ.json","graph_json":"https://pith.science/api/pith-number/4RPRORWNGKI6AQ2EELCXLCSBEQ/graph.json","events_json":"https://pith.science/api/pith-number/4RPRORWNGKI6AQ2EELCXLCSBEQ/events.json","paper":"https://pith.science/paper/4RPRORWN"},"agent_actions":{"view_html":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ","download_json":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ.json","view_paper":"https://pith.science/paper/4RPRORWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.5383&json=true","fetch_graph":"https://pith.science/api/pith-number/4RPRORWNGKI6AQ2EELCXLCSBEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4RPRORWNGKI6AQ2EELCXLCSBEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ/action/storage_attestation","attest_author":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ/action/author_attestation","sign_citation":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ/action/citation_signature","submit_replication":"https://pith.science/pith/4RPRORWNGKI6AQ2EELCXLCSBEQ/action/replication_record"}},"created_at":"2026-05-18T03:51:47.303937+00:00","updated_at":"2026-05-18T03:51:47.303937+00:00"}