Simplifying the axiomatization for the order affine geometry [article]

Dafa Li
<span title="2022-04-24">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Based on an ordering with directed lines and using constructions instead of existential axioms, von Plato proposed a constructive axiomatization of ordered affine geometry. There are 22 axioms for the ordered affine geometry, of which the axiom I.7 is about the convergence of three lines (ignoring their directions). In this paper, we indicate that the axiom I.7 includes much redundancy, and demonstrate that the complicated axiom I.7 can be replaced with a simpler and more intuitive new axiom
more &raquo; ... lled ODO) which describes the properties of oppositely and equally directed lines. We also investigate a possibility to replace the axiom I.6 with ODO.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:2205.05162v1</a> <a target="_blank" rel="external noopener" href="">fatcat:buqt2ocsnncvpg6od56ffyfcby</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="" title=" access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> </button> </a>