{"paper":{"title":"A Finitary Analogue of the Downward L\\\"owenheim-Skolem Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Abhisekh Sankaran","submitted_at":"2017-05-12T10:09:06Z","abstract_excerpt":"We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\\\"owenheim-Skolem property from classical model theory. We call this property as the *$\\mathcal{L}$-equivalent bounded substructure property*, denoted $\\mathcal{L}$-$\\mathsf{EBSP}$, where $\\mathcal{L}$ is either FO or MSO. Intuitively $\\mathcal{L}$-$\\mathsf{EBSP}$ states that a large finite structure contains a small \"logically similar\" substructure, where logical similarity means indistinguishability with respect to sentences of $\\mathcal{L}$ having a given quan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04493","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"}