{"paper":{"title":"A Version of $\\kappa$-Miller Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Heike Mildenberger, Saharon Shelah","submitted_at":"2018-02-22T11:36:06Z","abstract_excerpt":"Let $\\kappa$ be an uncountable cardinal such that $2^{<\\kappa} = \\kappa$ or just ${\\rm cf}(\\kappa) > \\omega$, $2^{2^{<\\kappa}}= 2^\\kappa$, and $([\\kappa]^\\kappa, \\supseteq)$ collapses $2^\\kappa$ to $\\omega$. We show under these assumptions the $\\kappa$-Miller forcing with club many splitting nodes collapses $2^\\kappa$ to $\\omega$ and adds a $\\kappa$-Cohen real."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07986","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"}