# 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

$(p,q,r)\in B$ only if $p,q$, and $r$ are collinear (all incident with a common line $\ell\in P_{1}$);

• 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 LinearOrderedGeometry 2013-03-22 17:19:35 2013-03-22 17:19:35 Mathprof (13753) Mathprof (13753) 4 Mathprof (13753) Definition msc 51G05