{"paper":{"title":"Various interplays between relation and cylindric algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-25T17:42:42Z","abstract_excerpt":"Using model theoretic techniques that proved that the class of $n$ neat reducts of $m$ dimensional cylindric algebras, $\\Nr_n\\CA_m$, is not elementary, we prove the same result for $\\Ra\\CA_k$, $k\\geq 5$, and we show that $\\Ra\\CA_k\\subset S_c\\Ra\\CA_k$ for all $k\\geq 5$. Conversely, using the rainbow construction for cylindric algebra, we show that several classes of algebras, related to the class $\\Nr_n\\CA_m$, $n$ finite and $m$ arbitrary, are not elementary. Our results apply to many cylindric-like algebras, including Pinter's substitution algebras and Halmos' polyadic algebras with and withou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5269","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"}