{"paper":{"title":"Some Banach spaces added by a Cohen real","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Mirna D\\v{z}amonja","submitted_at":"2014-09-29T16:15:54Z","abstract_excerpt":"We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density $\\aleph_1$ which does not embed into any such space in the ground model such a Banach space can be chosen to be UG This has consequences on the the isomorphic universality number for Banach spaces of density $\\aleph_1$, which is hence equal to $\\aleph_2$ in the standard Cohen model and the same is true for UG spaces. Analogous universality results for Banach spaces are true for other cardinals, by a different proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8172","kind":"arxiv","version":3},"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"}