{"paper":{"title":"The decision problem for a three-sorted fragment of set theory with restricted quantification and finite enumerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Domenico Cantone, Marianna Nicolosi-Asmundo","submitted_at":"2015-06-04T06:54:54Z","abstract_excerpt":"We solve the satisfiability problem for a three-sorted fragment of set theory (denoted $3LQST_0^R$), which admits a restricted form of quantification over individual and set variables and the finite enumeration operator $\\{\\text{-}, \\text{-}, \\ldots, \\text{-}\\}$ over individual variables, by showing that it enjoys a small model property, i.e., any satisfiable formula $\\psi$ of $3LQST_0^R$ has a finite model whose size depends solely on the length of $\\psi$ itself. Several set-theoretic constructs are expressible by $3LQST_0^R$-formulae, such as some variants of the power set operator and the u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01476","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"}