We can also strengthen PA1. Prove that any line in a Projective Geometry has at least 3 points. [Hint: You can avoid lot

[answerhappygod]

We can also strengthen PA1. Prove that any line in a Projective
Geometry has at least 3 points.
[Hint: You can avoid lots of little cases by not starting with PA1.
Let ℓ be a line and find some other lines
that must intersect it to find at least 3 points.]
Axioms:
(PA1) A line lies on at least two points.
(PA2) Any two distinct points lie on exactly one line.
(PA3) Any two distinct lines intersect in at least one point.
(PA4) There is a set of four points, no three of which are
collinear.