{"paper":{"title":"Preservation under Substructures modulo Bounded Cores","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Abhisekh Sankaran, Bharat Adsul, Pritish Kamath, Supratik Chakraborty, Vivek Madan","submitted_at":"2012-05-07T12:21:22Z","abstract_excerpt":"We investigate a model-theoretic property that generalizes the classical notion of \"preservation under substructures\". We call this property \\emph{preservation under substructures modulo bounded cores}, and present a syntactic characterization via $\\Sigma_2^0$ sentences for properties of arbitrary structures definable by FO sentences. As a sharper characterization, we further show that the count of existential quantifiers in the $\\Sigma_2^0$ sentence equals the size of the smallest bounded core. We also present our results on the sharper characterization for special fragments of FO and also ov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1358","kind":"arxiv","version":3},"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"}