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

This article is cited in 5 scientific papers (total in 5 papers)

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.

Full text: PDF file (292 kB)
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English version:
Algebra and Logic, 2008, 47:4, 242–257

Bibliographic databases:

UDC: 510.5+514.146
Received: 29.10.2007

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
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\by N.~T.~Kogabaev
\paper The class of projective planes is noncomputable
\jour Algebra Logika
\yr 2008
\vol 47
\issue 4
\pages 428--455
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\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}
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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  mathnet  crossref  mathscinet  isi
    2. N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra and Logic, 52:5 (2013), 355–366  mathnet  crossref  mathscinet  isi
    3. N. A. Bazhenov, “The branching theorem and computable categoricity in the Ershov hierarchy”, Algebra and Logic, 54:2 (2015), 91–104  mathnet  crossref  crossref  mathscinet  isi
    4. N. T. Kogabaev, “Freely generated projective planes with finite computable dimension”, Algebra and Logic, 55:6 (2017), 461–484  mathnet  crossref  crossref  isi
    5. A. K. Voǐtov, “The $\Delta^0_\alpha$-computable enumerations of the classes of projective planes”, Siberian Math. J., 59:2 (2018), 252–263  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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