{"paper":{"title":"Factoring a minimal ultrafilter into a thick part and a syndetic part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.RA"],"primary_cat":"math.LO","authors_text":"Neil Hindman, Will Brian","submitted_at":"2018-05-18T00:28:14Z","abstract_excerpt":"Let $S$ be an infinite discrete semigroup. The operation on $S$ extends uniquely to the Stone-\\v{C}ech compactification $\\beta S$ making $\\beta S$ a compact right topological semigroup with $S$ contained in its topological center. As such, $\\beta S$ has a smallest two sided ideal, $K(\\beta S)$. An ultrafilter $p$ on $S$ is \\emph{minimal} if and only if $p \\in K(\\beta S)$.\n  We show that any minimal ultrafilter $p$ factors into a thick part and a syndetic part. That is, there exist filters $\\mathcal F$ and $\\mathcal G$ such that $\\mathcal F$ consists only of thick sets, $\\mathcal G$ consists on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07000","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"}