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 Algebra Logika: Year: Volume: Issue: Page: Find

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

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 ÍØ-860.2014.1 Russian Foundation for Basic Research 14-01-0037613-01-91001-ÀÍÔ_à 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

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English version:
Algebra and Logic, 2015, 54:5, 387–407

Bibliographic databases:

UDC: 510.53+514.146

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
\Bibitem{Kog15} \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 \mathnet{http://mi.mathnet.ru/al715} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000366155000004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957973266} 

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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
2. N. T. Kogabaev, “Freely generated projective planes with finite computable dimension”, Algebra and Logic, 55:6 (2017), 461–484
3. N. Bazhenov, “Categoricity spectra for polymodal algebras”, Stud. Log., 104:6 (2016), 1083–1097
4. N. T. Kogabaev, “The embedding problem for computable projective planes”, Algebra and Logic, 56:1 (2017), 75–79
5. N. A. Bazhenov, “Effective categoricity for distributive lattices and Heyting algebras”, Lobachevskii J. Math., 38:4, SI (2017), 600–614
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