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Under CH and 2^{omega_1}> omega_2 we call an omega_1--tree a Jech--Kunen tree if it has kappa many branches for some kappa strictly between omega_1 and 2^{omega_1}. In this paper we prove that, assuming the existence of one inaccessible cardinal,\n  (1) it is consistent with CH plus 2^{omega_1}> omega_2 that there exist Kurepa trees and there are no Jech--Kunen trees,\n  (2) it is consistent with CH plus 2^{omega_1}= omega_4 that only Kurepa trees with omega_3 many branches exist.","authors_text":"Renling Jin, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1992-11-15T00:00:00Z","title":"Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9211214","kind":"arxiv","version":1},"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":"sha256:6dcb91a1c44c850451e844d5a4d03059a623ab731448fcaaaec9746ac38ea81d","target":"record","created_at":"2026-05-18T01:05:52Z","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":"12a19af15f62a3253d5f4149bf6e126e7a7f985dc395576d2952035cb5a6b7a8","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1992-11-15T00:00:00Z","title_canon_sha256":"01775e644b045ea898640dad7a57fe0b3aa43086b828462c95b6be9695ad2efe"},"schema_version":"1.0","source":{"id":"math/9211214","kind":"arxiv","version":1}},"canonical_sha256":"3cd971262e36cf05ea5e5c4b6ee174062eac13b204ea827ed17611f101077f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cd971262e36cf05ea5e5c4b6ee174062eac13b204ea827ed17611f101077f86","first_computed_at":"2026-05-18T01:05:52.447857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.447857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iCnhLzUmqzFJ3hdnfFDClcFBHv8j/5f5NlkA9J40RmYMzorHji2uLzFBjMWPdVfm8R6Xm4g7gHciemPpScytAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.448375Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9211214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dcb91a1c44c850451e844d5a4d03059a623ab731448fcaaaec9746ac38ea81d","sha256:159ae5c336da6667e5f437c2d809983b018e93cc27f118166e8fde0cc63a0255"],"state_sha256":"09a76ea829ace82072f80f572437eecc46bd52f167f7f8b4a47b6e646579f890"}