{"paper":{"title":"A solution to the finitizability problem for quantifier logics with equality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2015-03-01T23:46:48Z","abstract_excerpt":"We consider countable so-called rich subsemigroups of (\\omega\\omega,\\circ); each such semigroup $T$ gives a variety CPEA_T that is axiomatizable by a finite schema of equations taken in a countable subsignature of that of \\omega-dimensional cylindric-polyadic algebras with equality where substitutions are restricted to maps in T. It is shown that for any such T, A\\in CPEA_T iff A is representable as a concrete set algebra of \\omega-ary relations. The operations in the signature are set-theoretically interpreted like in polyadic equality set algebras, but such operations are relativized to a un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00376","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"}