{"paper":{"title":"Strongly proper forcing and some problems of Foreman","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monroe Eskew, Sean Cox","submitted_at":"2016-12-05T22:02:33Z","abstract_excerpt":"We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell's notion of \\emph{strongly proper} forcing. We prove: 1) Presaturation of a normal ideal implies projective antichain catching, enabling us to provide a solution to a problem from Foreman~\\cite{MR2768692} about ideal projections which is more comprehensive and simpler than the solution obtained in \\cite{MR3343538}. 2) We solve an older question from Foreman~\\cite{MR819932} about the relationship between generic hugeness and generic almost hugeness. 3) Finally, we provide solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01572","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"}