{"paper":{"title":"Approximation of subsets of natural numbers by c.e. sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Farzad Didehvar, Mohsen Mansouri","submitted_at":"2019-02-09T10:11:23Z","abstract_excerpt":"The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\\Delta_2$-approximation, as well as introducing the generically computable sets have been some efforts for this purpose. In this paper, a type of approximation for natural numbers subsets by computably enumerable sets will be examined. For an infinite and non-c.e set, $W_i$ will be an $A$.maximal (maximal inside $A$) if $W_i \\subseteq A$, is infinite and $\\forall j (W_i \\subseteq W_j \\subseteq A) \\to \\Delta (W_i, W_j )< \\infty$, where $\\Delta$ is the sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03399","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"}