{"paper":{"title":"Automorphisms of $\\mathscr{P}(\\lambda)/\\mathscr{I}_\\kappa$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Paul Larson, Paul McKenney","submitted_at":"2015-06-10T19:39:15Z","abstract_excerpt":"We study conditions on automorphisms of Boolean algebras of the form $P(\\lambda)/I_\\kappa$ (where $\\lambda$ is an uncountable cardinal and $I_\\kappa$ is the ideal of sets of cardinality less than $\\kappa$) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every cardinality-preserving automorphism of $P(2^\\kappa)/I_{\\kappa^+}$ which is trivial on all sets of cardinality $\\kappa^+$ is trivial, and that $MA_{\\aleph_1}$ implies that every automorphism of $P(\\mathbb{R})/Fin$ is trivial on a cocountable set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03433","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"}