{"paper":{"title":"On Strong Structural Completeness of Varieties and Quasivarieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Alex Citkin (Metropolitan Telecommunications, NewYork USA)","submitted_at":"2026-06-30T15:55:48Z","abstract_excerpt":"We study structural completeness in the infinitary sense (strong structural completeness) in an algebraic setting. A variety is structurally complete (SCpl) if it is generated, as a quasivariety, by its free algebras, and it is strongly structurally complete (SSCpl) if it is generated, as a prevariety, by its free algebras. A quasivariety is SSCpl if it is generated, as a prevariety, by its free algebras.\n  We prove that every quasivariety of finite type with the CEP that is generated by finite algebras and contains an infinite irreducible algebra is not SSCpl. Moreover, every congruence meet-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01271","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01271/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}