Axiom:Points are Between Themselves

Axiom

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

Let $=$ be the relation of equality.

Then the following axiom is imposed:

$\forall a,b: a = b \implies \mathsf{B}aba $

where $a$ and $b$ are points.

Intuition

If two points are the same, they are between themselves.

Sources

• June 1999: Alfred Tarski and Steven Givant: Tarski's System of Geometry (Bull. Symb. Log. Vol. 5, no. 2: pp. 175 – 214) : p. $185$ : Axiom $13$ (unnamed)