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.
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 difine the affine geometry on a ordered field,than prove that it satisfiedthe axiom of incidence, ordered and parallel of the Hilbert axiom system of geometry Thenwe difine the Euclidean geometry on Pythagoras field and prove that it satisfied farther theaxiom of congruence.
在本文中我们将定义有序域上的仿射几何，并证明它满足Ｈｉｌｂｅｒｔ几何公理体系的结合公理，顺序公理和平行公理。
Let Ω_F be the quaternary division ring imbedded by the ordered field F.
设Ｆ为有序域，Ω＿Ｆ是由Ｆ扩充而得的四元数除环。
Secondly,we introduce the order neighborhood semantics,give the frame conditions of the character axioms and inference rules of AKC,prove the frame soundness of AKC with respect to the frame conditions.
其次,我们引入有序邻域语义,给出描述AKC的特征公理和推理规则的框架条件,证明AKC相对这些框架条件是框架可靠的。