{"paper":{"title":"First order logic without equality on relativized semantics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Amitayu Banerjee, Mohamed Khaled","submitted_at":"2018-06-29T13:04:23Z","abstract_excerpt":"Let $\\alpha\\geq 2$ be any ordinal. We consider the class $\\mathsf{Drs}_{\\alpha}$ of relativized diagonal free set algebras of dimension $\\alpha$. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of $\\mathsf{Drs}_{\\alpha}$ are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class $\\mathsf{Drs}_{\\alpha}$ corresponds to first order logic, without equality symbol, with $\\alpha$-many variables and on relativized semantics. Hence, in this variati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00690","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"}