{"paper":{"title":"Essential Kurepa trees versus essential Jech---Kunen trees","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Renling Jin, Saharon Shelah","submitted_at":"1994-01-15T00:00:00Z","abstract_excerpt":"By an omega_1 --tree we mean a tree of size omega_1 and height omega_1. An omega_1 --tree is called a Kurepa tree if all its levels are countable and it has more than omega_1 branches. An omega_1 --tree is called a Jech--Kunen tree if it has kappa branches for some kappa strictly between omega_1 and 2^{omega_1}. A Kurepa tree is called an essential Kurepa tree if it contains no Jech--Kunen subtrees. A Jech--Kunen tree is called an essential Jech--Kunen tree if it contains no Kurepa subtrees. In this paper we prove that (1) it is consistent with CH and 2^{omega_1}> omega_2 that there exist esse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9401217","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"}