{"paper":{"title":"Towers in filters, cardinal invariants, and Luzin type families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnab\\'as Farkas, Jonathan Verner, J\\\"org Brendle","submitted_at":"2016-05-16T11:44:00Z","abstract_excerpt":"We investigate which filters on $\\omega$ can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in $[\\omega]^\\omega$). We prove the following results:\n  - Many classical examples of nice tall filters contain no towers (in ZFC).\n  - It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well).\n  - It is consistent that all towers generate non-meager filters, in particular (consistently) Borel filters do not contain towers.\n  - The statement \"Every ultrafilter contains towers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04735","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"}