Question: 1 describe a finite model such that no two lines...
1. Describe a finite model such that no two lines have the same set of incident points, axioms I2 and I3 are true, but I1 is false. Can you give a model as above with the additional constraint that for any two points, there are at least two lines incident to both?
Hint: It is doable with 4 points. 3 of them might be collinear. Pick some subsets of points cleverly and declare them to be lines. Make sure you don’t ruin I3 in the meantime.