Constructively presented projective planes (Q810866)

In an earlier paper [Commun. Algebra 16, No.11, 2209-2230 (1988; Zbl 0654.51002)] the author has given a finite presentation for projective planes by analogy to finitely presented groups. In this article he gives another definition for a presentation of projective planes: constructively presented planes \(<X/S,A>\). It is uniquely determined by a finite set of generating symbols X and a finite set of relations S, and by a choice algorithm A. The author shows that any finitely presented projective plane may be constructively finitely presented. In particular an example is given of constructively presented planes with nonsolvable word problem. Consequently the class of all constructively finitely presented planes is larger than the class of all finitely presented planes, because any finitely presented plane has a solvable word problem.