On finite weakly \(\{s,t\}\)-semiaffine linear spaces (Q1849903)

If \(({\mathcal P},{\mathcal L})\) is a finite linear space of order \(n\) with visible and invisible lines, then a point \(P\) is said to be ``good'' if \(P\) is such that all lines through it are visible. Let \(H\) be a finite set of non-negative integers. Then \(({\mathcal P},{\mathcal L})\) is said to be weakly \(H\)-semiaffine if the following conditions are satisfied: \noindent a) A line \(\ell\) is visible if and only if for every point \(P\not\in\ell\), the number \(\pi\) of lines through \(P\) and missing \(\ell\) is in \(H\); \noindent b) Every visible line has at least two good points; \noindent c) For any non-incident point-line pair \((P,\ell)\), \(\pi\geq\) min \(H\). \noindent In this paper \(\{s,t\}\)-semiaffine linear spaces are studied. The author classifies those \(\{s,t\}\)-semiaffine linear spaces with different point degree when a good point of degree \(n+1\) exists. In the other cases just some classes of them are classified.