If we remove a set of points from a projective plane we obtain a special incidence structure - called, according to Libois, a linear space - which satisfies the condition that any pair of points is joined by exactly one line. Each finite linear space \(\Sigma\) defines a set s of non-negative integers, precisely: if \(\pi\) (p,L) denotes the number of lines through the point p which are parallel to the line L, then \(s=\{\pi (p,L)| (p,L)\) is a non-incident point-line pair of \(\Sigma\) \(\}\). \(\Sigma\) is called s-semiaffine, too. The idea in this context is to show that, apart from degenerate cases, every finite s-semiaffine linear space is obtained from a projective plane by removing a suitable set of its points. The authors achieve this goal for \(\{\) 0,1,a\(\}\)-semiaffine linear spaces.
We note that some special \(\{\) 0,1,a\(\}\)-semiaffine linear spaces were studied by other authors.