{"paper":{"title":"Permutation groups containing infinite linear groups and reducts of infinite dimensional linear spaces over the two element field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bertalan Bodor, Csaba Szab\\'o, Kende Kalina","submitted_at":"2015-05-31T12:28:51Z","abstract_excerpt":"Let $\\mathbb{F}_2^\\omega$ denote the countably infinite dimensional vector space over the two element field and $\\operatorname{GL}(\\omega, 2)$ its automorphism group. Moreover, let $\\operatorname{Sym}(\\mathbb{F}_2^\\omega)$ denote the symmetric group acting on the elements of $\\mathbb{F}_2^\\omega$. It is shown that there are exactly four closed subgroups, $G$, such that $\\operatorname{GL}(\\omega, 2)\\leq G\\leq \\operatorname{Sym}(\\mathbb{F}_2^\\omega)$. As $\\mathbb{F}_2^\\omega$ is an $\\omega$-categorical (and homogeneous) structure, these groups correspond to the first order definable reducts of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00220","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"}