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 Algebra Logika, 2008, Volume 47, Number 4, Pages 428–455 (Mi al366)

The class of projective planes is noncomputable

N. T. Kogabaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Computable projective planes are investigated. It is stated that a free projective plane of countable rank in some inessential expansion is unbounded. This implies that such a plane has infinite computable dimension. The class of all computable projective planes is proved to be noncomputable (up to computable isomorphism).

Keywords: computable projective plane, free projective plane, computable class of structures, computable dimension of structure.

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English version:
Algebra and Logic, 2008, 47:4, 242–257

Bibliographic databases:

UDC: 510.5+514.146

Citation: N. T. Kogabaev, “The class of projective planes is noncomputable”, Algebra Logika, 47:4 (2008), 428–455; Algebra and Logic, 47:4 (2008), 242–257

Citation in format AMSBIB
\Bibitem{Kog08} \by N.~T.~Kogabaev \paper The class of projective planes is noncomputable \jour Algebra Logika \yr 2008 \vol 47 \issue 4 \pages 428--455 \mathnet{http://mi.mathnet.ru/al366} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2484563} \zmath{https://zbmath.org/?q=an:1164.03330} \transl \jour Algebra and Logic \yr 2008 \vol 47 \issue 4 \pages 242--257 \crossref{https://doi.org/10.1007/s10469-008-9015-z} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000259714200002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249138086} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. T. Kogabaev, “Noncomputability of classes of pappian and desarguesian projective planes”, Siberian Math. J., 54:2 (2013), 247–255
2. N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra and Logic, 52:5 (2013), 355–366
3. N. A. Bazhenov, “The branching theorem and computable categoricity in the Ershov hierarchy”, Algebra and Logic, 54:2 (2015), 91–104
4. N. T. Kogabaev, “Freely generated projective planes with finite computable dimension”, Algebra and Logic, 55:6 (2017), 461–484
5. A. K. Voǐtov, “The $\Delta^0_\alpha$-computable enumerations of the classes of projective planes”, Siberian Math. J., 59:2 (2018), 252–263
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