{"paper":{"title":"Enumeration Reducibility in Closure Spaces with Applications to Logic and Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.RA"],"primary_cat":"cs.DM","authors_text":"Emmanuel Jeandel (CARTE)","submitted_at":"2015-05-28T07:51:24Z","abstract_excerpt":"In many instances in first order logic or computable algebra, classical theorems  show that many problems are undecidable for general structures, but become  decidable if some rigidity is imposed on the structure.  For example, the set of theorems in many finitely axiomatisable theories is  nonrecursive, but the set of theorems for any finitely axiomatisable complete  theory is recursive.  Finitely presented groups might have an nonrecursive word problem, but  finitely presented simple groups have a recursive word problem.  In this article we introduce a topological framework based on closure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07578","kind":"arxiv","version":3},"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"}