{"paper":{"title":"A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Aleksandar Pavlovi\\'c, Milo\\v{s} S. Kurili\\'c","submitted_at":"2013-01-23T22:03:54Z","abstract_excerpt":"We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\\lambda_s$ (the algebraic convergence) and $\\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\\lambda_{ls}$ is weakly topological if B satisfies condition $(\\hbar)$ (implied by the ${\\mathfrak t}$-cc). On the other hand, if $\\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\\mathfrak h}$-cc alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5658","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"}