{"paper":{"title":"Generalized symmetric systems and thin-very tall compact scattered spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Miguel Angel Mota, William Weiss","submitted_at":"2015-07-14T21:00:42Z","abstract_excerpt":"We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal $\\kappa \\geq \\omega$, there is a poset $\\mathcal P_\\kappa$ preserving all cardinals and forcing the existence of a $\\kappa$--thin very tall locally compact scattered space. For $\\kappa > \\omega$, we conceive the poset $\\mathcal P_\\kappa$ as a higher analogue of the poset $\\mathcal P_\\omega$ originally introduced by Asper\\'{o} and Bagaria in the context of an (unpublished) alternative consistency proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04026","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"}