{"paper":{"title":"Merging $\\lim^1 \\mathbf{A} \\ne 0$ with other nonvanishing constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.LO","authors_text":"Justin Tatch Moore, Nathaniel Bannister","submitted_at":"2026-07-04T19:33:35Z","abstract_excerpt":"We develop methods for forcing $\\lim^1 \\mathbf{A} \\ne 0$, where $\\mathbf{A}$ is a particular inverse system of abelian groups introduced by Marde\\v{s}i\\'c and Prasolov in their computation of certain strong homology groups. These methods allow us to extend previous nonvanishing results of Casarosa and Lambie-Hanson for $\\lim^k \\mathbf{A}$ for $k \\geq 2$. Specifically we show that, for a given $n$, it is relatively consistent with ZFC that $\\mathfrak{b} = \\mathfrak{d} = \\omega_n$ and $\\lim^k \\mathbf{A} \\ne 0$ whenever $1 \\leq k \\leq n$ (previously established with $2 \\leq k \\leq n$). We also sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03995","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03995/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}