Some algorithmic problems for projective planes (Q1073331)

A. I. Shirshov at the 14th All-Union Algebra Conference in 1977 formulated the following question: Is the equality problem for Pappian projective planes and for Desarguesian projective planes algorithmically decidable? Using the results of \textit{A. Macintyre} [J. Symbolic Logic 38, 428-436 (1973; Zbl 0286.02046) and Proc. Lond. Math. Soc., III. Ser. 39, 211-236 (1979; Zbl 0433.16018)] the author of this paper shows that for Pappian projective planes the equality problem is algorithmically decidable and there is a finitely generated Desarguesian projective plane with undecidable equality problem. This work is of interest in connection with the author's earlier works [Algebra Logic 20, 277-282 (1982); translation from Algebra Logika 20, No.4, 419-426 (1981; Zbl 0505.51008) and Algebra Logic 22, 45-47 (1983); translation from Algebra Logika 22, No.1, 61-78 (1983; Zbl 0553.51002)].