{"paper":{"title":"Constructing Ultrapowers from Elementary Extensions of Full Clones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Joseph Van Name","submitted_at":"2012-06-30T17:20:03Z","abstract_excerpt":"Let $A$ be an infinite set. Let $\\Omega(A)$ be the algebra over $A$ where every constant is a fundamental constant and every finitary function is a fundamental operation. We shall give a method of representing any algebra $\\mathcal{L}$ in the variety generated by $\\Omega(A)$ as limit reduced powers and even direct limits of limit reduced powers of $\\mathcal{L}$. If the algebra $\\mathcal{L}$ is elementarily equivalent to $\\Omega(A)$, then this construction represents $\\Omega(A)$ as a limit ultrapower and also as direct limits of limit ultrapowers of $\\Omega(A)$. This method therefore gives a me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0118","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"}