{"paper":{"title":"Knots, Braids and First Order Logic","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.LO","authors_text":"Siddhartha Gadgil, T. V. H. Prathamesh","submitted_at":"2012-09-17T06:49:35Z","abstract_excerpt":"Determining when two knots are equivalent (more precisely isotopic) is a fundamental problem in topology. Here we formulate this problem in terms of Predicate Calculus, using the formulation of knots in terms of braids and some basic topological results.\n  Concretely, Knot theory is formulated in terms of a language with signature $(\\cdot,T,\\equiv, 1,\\sigma,\\bar\\sigma)$, with $\\cdot$ a 2-function, $T$ a 1-function, $\\equiv$ a 2-predicate and 1, $\\sigma$ and $\\bar\\sigma$ constants. We describe a finite set of axioms making the language into a (first order) theory. We show that every knot can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3562","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"}