Geodesic
Undecidability of the theory of projective planes
Algebra i logika, Tome 49 (2010) no. 1, pp. 3-17

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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.
Keywords: projective plane, freely generated projective plane, undecidable theory. 
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     title = {Undecidability of the theory of projective planes},
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N. T. Kogabaev. Undecidability of the theory of projective planes. Algebra i logika, Tome 49 (2010) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/AL_2010_49_1_a0/