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Undecidability of the theory of projective planes. (English. Russian original) Zbl 1195.03043
Algebra Logic 49, No. 1, 1-11 (2010); translation from Algebra Logika 49, No. 1, 3-17 (2010).
Summary: Elementary theories of projective planes are studied. The class of symmetric irreflexive graphs is proved to be relatively elementarily definable in the class of projective planes. Therefore, the theory of projective planes is hereditarily undecidable.

03D35 Undecidability and degrees of sets of sentences
51M99 Real and complex geometry
Full Text: DOI
[1] A. I. Shirshov and A. A. Nikitin, ”Toward a theory of projective planes,” Algebra Logika, 20, No. 3, 330-356 (1981). · Zbl 0505.51007
[2] A. I. Shirshov and A. A. Nikitin, Algebraic Theory of Projective Planes [in Russian], NGU, Novosibirsk (1987). · Zbl 0692.51001
[3] Yu. L. Ershov, I. A. Lavrov, A. D. Taimanov, and M. A. Taitslin, ”Elementary theories,” Usp. Mat. Nauk, 20, No. 4, 37-108 (1965). · Zbl 0199.03001
[4] A. A. Nikitin, ”Freely generated projective planes,” Algebra Logika, 22, No. 1, 61-77 (1983). · Zbl 0553.51002
[5] Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], 2nd edn., Nauka, Moscow (1987).
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