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Fundam. Prikl. Mat., 2004, Volume 10, Issue 4, Pages 107–157 (Mi fpm786)  

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

Model-theoretic properties of regular polygons

A. V. Mikhaleva, E. V. Ovchinnikovab, E. A. Palyutinc, A. A. Stepanovad

a M. V. Lomonosov Moscow State University
b Novosibirsk State Technical University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
d Far Eastern National University

Abstract: This work is devoted to results obtained in the model theory of regular polygons. We give a characterization of monoids with axiomatizable and model-complete class of regular polygons. We describe the monoids with complete class of regular polygons that satisfy some additional conditions. We study the monoids whose regular core is represented as a union of finitely many principal right ideals and all regular polygons over which have a stable and superstable theory. We prove the stability of the class of all regular polygons over a monoid provided this class is axiomatizable and model-complete. We also describe the monoids for which the class of all regular polygons is superstable and $\omega$-stable provided this class is axiomatizable and model-complete.

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English version:
Journal of Mathematical Sciences (New York), 2007, 140:2, 250–285

Bibliographic databases:

UDC: 510.67+512.56

Citation: A. V. Mikhalev, E. V. Ovchinnikova, E. A. Palyutin, A. A. Stepanova, “Model-theoretic properties of regular polygons”, Fundam. Prikl. Mat., 10:4 (2004), 107–157; J. Math. Sci., 140:2 (2007), 250–285

Citation in format AMSBIB
\Bibitem{MikOvcPal04}
\by A.~V.~Mikhalev, E.~V.~Ovchinnikova, E.~A.~Palyutin, A.~A.~Stepanova
\paper Model-theoretic properties of regular polygons
\jour Fundam. Prikl. Mat.
\yr 2004
\vol 10
\issue 4
\pages 107--157
\mathnet{http://mi.mathnet.ru/fpm786}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2142512}
\zmath{https://zbmath.org/?q=an:1073.03020}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 140
\issue 2
\pages 250--285
\crossref{https://doi.org/10.1007/s10958-007-0422-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845788326}


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    This publication is cited in the following articles:
    1. V. Gould, A. V. Mikhalev, E. A. Palyutin, A. A. Stepanova, “Model-theoretic properties of free, projective, and flat $S$-acts”, J. Math. Sci., 164:2 (2010), 195–227  mathnet  crossref  mathscinet
    2. M. A. Pervukhin, “O regulyarnykh chastichno uporyadochennykh poligonakh”, Vestn. NGU. Ser. matem., mekh., inform., 9:4 (2009), 70–75  mathnet
    3. A. A. Stepanova, G. I. Baturin, “Regular $S$-acts with primitive normal and antiadditive theories”, J. Math. Sci., 185:3 (2012), 497–503  mathnet  crossref
    4. A. A. Stepanova, “Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group”, Siberian Math. J., 56:3 (2015), 516–525  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. E. L. Efremov, A. A. Stepanova, “Axiomatizability of the class of weakly injective $S$-acts”, Siberian Math. J., 58:4 (2017), 611–618  mathnet  crossref  crossref  isi  elib  elib
  • Фундаментальная и прикладная математика
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