论文标题
简化订单仿射几何形状的公理化
Simplifying the axiomatization for the order affine geometry
论文作者
论文摘要
冯·柏拉图（Von Plato）基于有针线和使用构造代替存在的公理的订购，并提出了有序仿射几何形状的建设性公理化。有22个公理用于有序的仿射几何形状，其中公理I.7是关于三条线的收敛性（忽略它们的方向）。在本文中，我们指出公理I.7包括很多冗余，并证明可以用更简单，更直观的新公理（称为ODO）代替复杂的公理i.7，该公理（称为ODO）描述了相反和平等定向线的性质。我们还研究了用ODO替换公理I.6的可能性。
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 (called ODO) which describes the properties of oppositely and equally directed lines. We also investigate a possibility to replace the axiom I.6 with ODO.
