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linear ordered geometry (Definition)

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)$.



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Cross-references: line, incident, collinear, points, strict betweenness relation, incidence geometry
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This is version 1 of linear ordered geometry, born on 2007-06-25.
Object id is 9678, canonical name is LinearOrderedGeometry2.
Accessed 513 times total.

Classification:
AMS MSC51G05 (Geometry :: Ordered geometries )

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