Computable dimensions of Pappusian and Desarguesian projective planes |
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| Authors: | N. T. Kogabaev |
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| Affiliation: | 1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
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| Abstract: | Computable presentations of projective planes are studied. Based on an interpretation of a class of fields (associative skew fields) within a class of Pappusian (Desarguesian) projective planes, it is proved that the question whether there exists a computable presentation for a Pappusian (Desarguesian) projective plane reduces to asking if there exists a computable presentation for a corresponding field (associative skew field). It is stated that the computable dimension of a Pappusian (Desarguesian) projective plane coincides with that of a corresponding field (associative skew field). |
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