{"paper":{"title":"Semigroups in Stable Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yatir Halevi","submitted_at":"2015-09-08T08:07:22Z","abstract_excerpt":"Assume $G$ is a definable group in a stable structure $M$. Newelski showed that the semigroup $S_G(M)$ of complete types concentrated on $G$ is an inverse limit of the $\\infty$-definable (in $M^{eq}$) semigroups $S_{G,\\Delta}(M)$. He also shows that it is strongly $\\pi$-regular: for every $p\\in S_{G,\\Delta}(M)$ there exists $n\\in\\mathbb{N}$ such that $p^n$ is in a subgroup of $S_{G,\\Delta}(M)$. We show that $S_{G,\\Delta}(M)$ is in fact an intersection of definable semigroups, so $S_G(M)$ is an inverse limit of definable semigroups and that the latter property is enjoyed by all $\\infty$-definab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02275","kind":"arxiv","version":2},"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"}