{"paper":{"title":"On first-order expressibility of satisfiability in submodels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Denis I. Saveliev","submitted_at":"2019-03-12T15:25:19Z","abstract_excerpt":"Let $\\kappa,\\lambda$ be regular cardinals, $\\lambda\\le\\kappa$, let $\\varphi$ be a sentence of the language $\\mathcal L_{\\kappa,\\lambda}$ in a given signature, and let $\\vartheta(\\varphi)$ express the fact that $\\varphi$ holds in a submodel, i.e., any model $\\mathfrak A$ in the signature satisfies $\\vartheta(\\varphi)$ if and only if some submodel $\\mathfrak B$ of $\\mathfrak A$ satisfies $\\varphi$. It was shown in [1] that, whenever $\\varphi$ is in $\\mathcal L_{\\kappa,\\omega}$ in the signature having less than $\\kappa$ functional symbols (and arbitrarily many predicate symbols), then $\\vartheta("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04993","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"}