Axiom:Upper Dimensional Axiom

Axiom
Let $a,b,c,...,x,y,z$ be points.

Let $\mathsf{B}$ be the relation of betweenness.

Let $=$ be the relation of equality.

0-Dimensions
Let the universe of discourse be a 0-dimensional space.


 * $\forall a,b: a = b$

Intuition
There is only one point.

1-Dimension
Let the universe of discourse be a 1-dimensional space.


 * $\forall a,b,c: \mathsf{B}abc \lor \mathsf{B}bca \lor \mathsf{B}cab$.

Intuition
Any three points are collinear.