{"paper":{"title":"Distributivity and Minimality in Perfect Tree Forcings for Singular Cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Heike Mildenberger, Maxwell Levine","submitted_at":"2021-10-07T17:38:43Z","abstract_excerpt":"Dobrinen, Hathaway and Prikry studied a forcing $\\mathbb{P}_\\kappa$ consisting of perfect trees of height $\\lambda$ and width $\\kappa$ where $\\kappa$ is a singular $\\omega$-strong limit of cofinality $\\lambda$. They showed that if $\\kappa$ is singular of countable cofinality, then $\\mathbb{P}_\\kappa$ is minimal for $\\omega$-sequences assuming that $\\kappa$ is a supremum of a sequence of measurable cardinals. We obtain this result without the measurability assumption.\n  Prikry proved that $\\mathbb{P}_\\kappa$ is $(\\omega,\\nu)$-distributive for all $\\nu<\\kappa$ given a singular $\\omega$-strong li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.03648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}