{"paper":{"title":"Planting Kurepa trees and killing Jech-Kunen trees in a model by using one inaccessible cardinal","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Renling Jin, Saharon Shelah","submitted_at":"1992-11-15T00:00:00Z","abstract_excerpt":"By an omega_1--tree we mean a tree of power omega_1 and height omega_1. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9211214","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"}