Alternative axiomatization I

Task number: 3893

Show that in the definition of the projective plane, the axiom of the existence of four points in the general position can be replaced by one of the following axioms, while the modified set will again define finite projective planes:

  • Variant

    There are two different lines with at least three points, formally: \(\exists P,Q \in \mathcal P: P \not= Q \wedge |P| \geq 3 \wedge |Q| \geq 3\).

  • Variant

    \(X\) cannot be covered by two lines.

Difficulty level: Moderate task
Proving or derivation task
Cs translation
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