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Algebra Logika, 2015, Volume 54, Number 5, Pages 599–627 (Mi al715)  

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

The theory of projective planes is complete with respect to degree spectra and effective dimensions

N. T. Kogabaevab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We prove that the theory of Pappian projective planes is complete with respect to degree spectra of automorphically nontrivial structures, effective dimensions, degree spectra of relations, categoricity spectra, and automorphism spectra. Therefore, for every natural $n\ge2$, there exists a computable Pappian projective plane with computable dimension $n$.

Keywords: projective plane, Pappian projective plane, computable structure, degree spectrum of structure, computable dimension, degree spectrum of relation, categoricity spectrum, automorphism spectrum.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-860.2014.1
Russian Foundation for Basic Research 14-01-00376
13-01-91001-АНФ_а
Supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-860.2014.1) and by RFBR (projects No. 14-01-00376 and 13-01-91001-ANF_a).


DOI: https://doi.org/10.17377/alglog.2015.54.504

Full text: PDF file (260 kB)
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English version:
Algebra and Logic, 2015, 54:5, 387–407

Bibliographic databases:

UDC: 510.53+514.146
Received: 26.10.2014

Citation: N. T. Kogabaev, “The theory of projective planes is complete with respect to degree spectra and effective dimensions”, Algebra Logika, 54:5 (2015), 599–627; Algebra and Logic, 54:5 (2015), 387–407

Citation in format AMSBIB
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\by N.~T.~Kogabaev
\paper The theory of projective planes is complete with respect to degree spectra and effective dimensions
\jour Algebra Logika
\yr 2015
\vol 54
\issue 5
\pages 599--627
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\crossref{https://doi.org/10.17377/alglog.2015.54.504}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468420}
\transl
\jour Algebra and Logic
\yr 2015
\vol 54
\issue 5
\pages 387--407
\crossref{https://doi.org/10.1007/s10469-015-9360-7}
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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, “$\Pi^1_1$-completeness of the computable categoricity problem for projective planes”, Algebra and Logic, 55:4 (2016), 283–288  mathnet  crossref  crossref  isi
    2. N. T. Kogabaev, “Freely generated projective planes with finite computable dimension”, Algebra and Logic, 55:6 (2017), 461–484  mathnet  crossref  crossref  isi
    3. N. Bazhenov, “Categoricity spectra for polymodal algebras”, Stud. Log., 104:6 (2016), 1083–1097  crossref  mathscinet  zmath  isi  scopus
    4. N. T. Kogabaev, “The embedding problem for computable projective planes”, Algebra and Logic, 56:1 (2017), 75–79  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. N. A. Bazhenov, “Effective categoricity for distributive lattices and Heyting algebras”, Lobachevskii J. Math., 38:4, SI (2017), 600–614  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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