{"paper":{"title":"A solution to Roitman's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Heike Mildenberger","submitted_at":"2014-04-29T13:03:17Z","abstract_excerpt":"We answer Question~3.2 from Shelah \\cite{Sh:666}: Given a maximal almost disjoint (mad) family $\\mathcal A$ of size $\\aleph_1$, we construct a forcing ${\\mathbb Q}(\\mathcal A)$ that has Axiom A, is ${}^\\omega \\omega$-bounding, preserves selective ultrafilters, has the $\\aleph_2$-properness isomorphism condition (p.i.c.), and destroys the mad family $\\mathcal A$. We develop a new construction technique for partial orders, combining ladder systems for $\\omega_1$ with trees of normed creatures.\n  Countable support iteration of the new kind of iterands solves Roitman's problem in the case of $d=\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7343","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"}