linear ordered geometry
An incidence geometry $A=(P,n,I)$ is a linear ordered geometry if there is a strict betweenness relation $B$ defined on the points ${P}_{0}$ of $A$, such that
 Col1

Col2
for any pairwise distinct collinear points $p,q,r$, at least one of $(p,q,r)$, $(q,r,p)$, or $(r,p,q)\in B$,
We denote the linear ordered geometry by $(A,B)$.
Title  linear ordered geometry 

Canonical name  LinearOrderedGeometry 
Date of creation  20130322 17:19:35 
Last modified on  20130322 17:19:35 
Owner  Mathprof (13753) 
Last modified by  Mathprof (13753) 
Numerical id  4 
Author  Mathprof (13753) 
Entry type  Definition 
Classification  msc 51G05 