{"paper":{"title":"Small sets in Mann pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pantelis E. Eleftheriou","submitted_at":"2018-12-19T14:24:33Z","abstract_excerpt":"Let $\\widetilde{\\mathcal M}=\\langle \\mathcal M, G\\rangle$ be an expansion of a real closed field $\\mathcal M$ by a dense subgroup $G$ of $\\langle M^{>0}, \\cdot\\rangle$ with the Mann property. We prove that the induced structure on $G$ by $\\mathcal M$ eliminates imaginaries. As a consequence, every small set $X$ definable in $\\mathcal M$ can be definably embedded into some $G^l$, uniformly in parameters. These results are proved in a more general setting, where $\\widetilde{\\mathcal M}=\\langle \\mathcal M, P\\rangle$ is an expansion of an o-minimal structure $\\mathcal M$ by a dense set $P\\subseteq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07970","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"}