{"paper":{"title":"Trivial automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ilijas Farah, Saharon Shelah","submitted_at":"2011-12-15T17:18:46Z","abstract_excerpt":"We prove that the statement `For all Borel ideals I and J on $\\omega$, every isomorphism between Boolean algebras $P(\\omega)/I$ and $P(\\omega)/J$ has a continuous representation' is relatively consistent with ZFC. In this model every isomorphism between $P(\\omega)/I$ and any other quotient $P(\\omega)/J$ over a Borel ideal is trivial for a number of Borel ideals I on $\\omega$.\n  We can also assure that the dominating number is equal to $\\aleph_1$ and that $2^{\\aleph_1}>2^{\\aleph_0}$. Therefore the Calkin algebra has outer automorphisms while all automorphisms of $P(\\omega)/Fin$ are trivial.\n  P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3571","kind":"arxiv","version":2},"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"}