{"paper":{"title":"Can a small forcing create Kurepa trees?","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Renling Jin, Saharon Shelah","submitted_at":"1995-04-15T00:00:00Z","abstract_excerpt":"In the paper we probe the possibilities of creating a Kurepa tree in a generic extension of a model of CH plus no Kurepa trees by an omega_1-preserving forcing notion of size at most omega_1. In the first section we show that in the Levy model obtained by collapsing all cardinals between omega_1 and a strongly inaccessible cardinal by forcing with a countable support Levy collapsing order many omega_1-preserving forcing notions of size at most omega_1 including all omega-proper forcing notions and some proper but not omega-proper forcing notions of size at most omega_1 do not create Kurepa tre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9504220","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"}