{"paper":{"title":"Adding a lot of Cohen reals by adding a few","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Moti Gitik","submitted_at":"1995-07-05T00:00:00Z","abstract_excerpt":"The purpose of the paper is to produce models V_1 \\subset V_2 such that adding kappa-many Cohen reals to V_2 adds lambda Cohen reals to V_1. Some of the results:\n  1. Suppose that V satisfies GCH, kappa = \\cup kappa_n= \\cup o(kappa_n). Then there is a cardinal preserving generic extension V_1 of V satisfying GCH and having the same reals as V does , so that adding kappa many Cohen reals over V_1 produces kappa^+ Cohen reals over V.\n  2. Suppose that V is a model of GCH. Then there is a cofinality preserving extension V_1 satisfying GCH so that adding a Cohen real to V_1 produces aleph_1 Cohen "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507209","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"}