{"paper":{"title":"Epic substructures and primitive positive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Miguel Campercholi","submitted_at":"2016-07-11T20:20:41Z","abstract_excerpt":"For $\\mathbf{A}\\leq\\mathbf{B}$ first order structures in a class $\\mathcal{K}$, say that $\\mathbf{A}$ is an epic substructure of $\\mathbf{B}$ in $\\mathcal{K}$ if for every $\\mathbf{C}\\in\\mathcal{K}$ and all homomorphisms $g,g^{\\prime}:\\mathbf{B}\\rightarrow\\mathbf{C}$, if $g$ and $g'$ agree on $A$, then $g=g'$. We prove that $\\mathbf{A}$ is an epic substructure of $\\mathbf{B}$ in a class $\\mathcal{K}$ closed under ultraproducts if and only if $A$ generates $\\mathbf{B}$ via operations definable in $\\mathcal{K}$ with primitive positive formulas. Applying this result we show that a quasivariety of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03139","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"}