{"paper":{"title":"$\\aleph_0$-categoricity of semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.LO","authors_text":"Thomas Quinn-Gregson, Victoria Gould","submitted_at":"2018-02-15T18:53:56Z","abstract_excerpt":"In this paper we initiate the study of $\\aleph_0$-categorical semigroups, where a countable semigroup $S$ is $\\aleph_0$-categorical if, for any natural number $n$, the action of its group of automorphisms Aut $S$ on $S^n$ has only finitely many orbits. We show that $\\aleph_0$-categoricity transfers to certain important substructures such as maximal subgroups and principal factors. We examine the relationship between $\\aleph_0$-categoricity and a number of semigroup and monoid constructions, namely direct sums, 0-direct unions, semidirect products and $\\mathcal{P}$-semigroups. As a corollary, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05703","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"}