Geodesic
The complexity of isomorphism problem for computable projective planes
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 68-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Computable presentations for projective planes are studied. We prove that the isomorphism problem is $\Sigma^1_1$ complete for the following classes of projective planes: pappian projective planes, desarguesian projective planes, arbitrary projective planes.
Keywords: projective plane, pappian projective plane, desarguesian projective plane, computable model, isomorphism problem. 
@article{VNGU_2013_13_1_a6,
     author = {N. T. Kogabaev},
     title = {The complexity of isomorphism problem for computable projective planes},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {68--75},
     year = {2013},
     volume = {13},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a6/}
}
TY  - JOUR
AU  - N. T. Kogabaev
TI  - The complexity of isomorphism problem for computable projective planes
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2013
SP  - 68
EP  - 75
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a6/
LA  - ru
ID  - VNGU_2013_13_1_a6
ER  - 
%0 Journal Article
%A N. T. Kogabaev
%T The complexity of isomorphism problem for computable projective planes
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2013
%P 68-75
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a6/
%G ru
%F VNGU_2013_13_1_a6
N. T. Kogabaev. The complexity of isomorphism problem for computable projective planes. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 68-75. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a6/

[1] Morozov A. S., “Funktsionalnye derevya i avtomorfizmy modelei”, Algebra i logika, 32:1 (1993), 54–72 | MR | Zbl

[2] Nies A., “Undecidable Fragments of Elementary Theories”, Algebra Univers., 35:1 (1996), 8–33 | DOI | MR | Zbl

[3] Goncharov S. S., Nait Dzh., “Vychislimye strukturnye i antistrukturnye teoremy”, Algebra i logika, 41:6 (2002), 639–681 | MR | Zbl

[4] Hirschfeldt D., Khoussainov B., Shore R., Slinko A. M., “Degree Spectra and Computable Dimensions in Algebraic Structures”, Ann. Pure Appl. Logic, 115:1–3 (2002), 71–113 | DOI | MR | Zbl

[5] Calvert W., “The Isomorphism Problem for Classes of Computable Fields”, Arch. Math. Logic, 43:3 (2004), 327–336 | DOI | MR | Zbl

[6] Calvert W., “The Isomorphism Problem for Computable Abelian $p$-Groups of Bounded Length”, J. Symb. Logic, 70:1 (2005), 331–345 | DOI | MR | Zbl

[7] Shirshov A. I., Nikitin A. A., “K teorii proektivnykh ploskostei”, Algebra i logika, 20:3 (1981), 330–356 | MR | Zbl

[8] Shirshov A. I., Nikitin A. A., Algebraicheskaya teoriya proektivnykh ploskostei, Ucheb. posobie, Novosibirsk, 1987 | Zbl

[9] Goncharov S. S., Ershov Yu. L., Konstruktivnye modeli, Nauch. kn., Novosibirsk, 1999

[10] Hughes D. R., Piper F. C., Projective Planes, Springer, 1973 | MR | Zbl

[11] Fokina E. B., Friedman S. D., Harizanov V., Knight J. F., McCoy C., Montalbán A., “Isomorphism Relations on Computable Structures”, J. Symb. Logic, 77:1 (2012), 122–132 | DOI | MR | Zbl