{"paper":{"title":"Ways of Destruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnabas Farkas, Lyubomyr Zdomskyy","submitted_at":"2018-12-04T15:21:36Z","abstract_excerpt":"We study the following natural strong variant of destroying Borel ideals: $\\mathbb{P}$ $\\textit{$+$-destroys}$ $\\mathcal{I}$ if $\\mathbb{P}$ adds an $\\mathcal{I}$-positive set which has finite intersection with every $A\\in\\mathcal{I}\\cap V$. Also, we discuss the associated variants \\begin{align*} \\mathrm{non}^*(\\mathcal{I},+)=&\\min\\big\\{|\\mathcal{Y}|:\\mathcal{Y}\\subseteq\\mathcal{I}^+,\\; \\forall\\;A\\in\\mathcal{I}\\;\\exists\\;Y\\in\\mathcal{Y}\\;|A\\cap Y|<\\omega\\big\\}\\\\ \\mathrm{cov}^*(\\mathcal{I},+)=&\\min\\big\\{|\\mathcal{C}|:\\mathcal{C}\\subseteq\\mathcal{I},\\; \\forall\\;Y\\in\\mathcal{I}^+\\;\\exists\\;C\\in\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01480","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":""},"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"}