代数结构与几何基础Ⅲ——射影几何的公理体系

Algebraic Structure and Foundation of Geometry Ⅲ Axioms of projective geometry

在本文中我们将给出只保留结合公理的几何,并证明:这种几何.同构于域上的射影几何,若添加顺序公理,则得到同构于有序域上的射影几何的几何.

In this paper, we give a geometry which satisfies only the axioms of incidence, and prove that this geometry is omorphic to the projective geometry over a field. If the above geometry satisfies also the axioms of order,then we obtain a geometry which is isomorphic to projective geometry over a ordered field.