{"paper":{"title":"Effective inseparability, lattices, and pre-ordering relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrea Sorbi, Uri Andrews","submitted_at":"2019-01-18T08:57:18Z","abstract_excerpt":"We study effectively inseparable (e.i.) pre-lattices (i.e. structures of the form $L=\\langle \\omega, \\wedge, \\lor, 0, 1, \\leq_L\\rangle$ where $\\omega$ denotes the set of natural numbers and the following hold: $\\wedge, \\lor$ are binary computable operations; $\\leq_L$ is a c.e. pre-ordering relation, with $0 \\leq_{L} x \\leq_{L} 1$ for every $x$; the equivalence relation $\\equiv_L$ originated by $\\leq_L$ is a congruence on $L$ such that the corresponding quotient structure is a non-trivial bounded lattice; the $\\equiv_L$-equivalence classes of $0$ and $1$ form an effectively inseparable pair), a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06136","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"}