Axiom:Identity of Betweenness
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Axiom
Let $\mathsf{B}$ be the relation of betweenness.
Let $=$ be the relation of equality.
Then the following axiom holds:
- $\forall a,b: \mathsf{B}aba \implies a = b$
where $a$ and $b$ are points.
Intuition
If between a point and itself lies another point, we're dealing with exactly one point.
Sources
- June 1999: Alfred Tarski and Steven Givant: Tarski's System of Geometry (Bull. Symb. Log. Vol. 5, no. 2: pp. 175 – 214) : p. $179$ : Axiom $6$