On freely generated projective planes (Q802135)

The author describes a construction of the projective plane freely generated by a given nondegenerate nonclosed configuration (i.e. partial projective plane), using the representation of a projective plane as a heterogeneous algebra [\textit{A. I. Shirshov} and \textit{A. A. Nikitin}, Algebra Logika 20, No.3, 330-356 (1981; Zbl 0505.51007)]. Relying on this result, it is proved that for the projective planes freely generated by a finite nondegenerate nonclosed configuration the problem of incidence [cf. \textit{S. Földes} and \textit{N. Singhi}, Geom. Dedicata 9, 497-499 (1980; Zbl 0514.03017)], the problem of equality, the problem of embedding an element in a subplane, and the problem of intersection of subplanes are algorithmically solvable. It is also shown that every freely generated projective plane is approximated by any finitely generated projective plane.