{"paper":{"title":"$2^{\\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of Sym$(\\mathbb{N})$ via the classification of the reducts of the Henson digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.LO","authors_text":"Lovkush Agarwal, Michael Kompatscher","submitted_at":"2015-09-25T11:02:44Z","abstract_excerpt":"Given two structures $\\mathcal{M}$ and $\\mathcal{N}$ on the same domain, we say that $\\mathcal{N}$ is a reduct of $\\mathcal{M}$ if all $\\emptyset$-definable relations of $\\mathcal{N}$ are $\\emptyset$-definable in $\\mathcal{M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are $\\aleph_0$-categorical, determining their reducts is equivalent to determining all closed supergroups $G<$ Sym$(\\mathbb{N})$ of their automorphism groups.\n  A consequence of the classif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07674","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"}