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Algebras of Distributions of Binary Isolating Formulas for Quite o-Minimal Theories

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Algebra and Logic Aims and scope

Algebras of distributions of binary isolating formulas over a type for quite o-minimal theories with nonmaximal number of countable models are described. It is proved that an isomorphism of these algebras for two 1-types is characterized by the coincidence of convexity ranks and also by simultaneous satisfaction of isolation, quasirationality, or irrationality of those types. It is shown that for quite o-minimal theories with nonmaximum many countable models, every algebra of distributions of binary isolating formulas over a pair of nonweakly orthogonal types is a generalized commutative monoid.

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References

  1. D. Yu. Emel’yanov, B. Sh. Kulpeshov, and S. V. Sudoplatov, “Algebras of distributions for binary formulas in countably categorical weakly o-minimal structures,” Algebra and Logic, Vol. 56, No. 1, 13-36 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Macpherson, D. Marker, and Ch. Steinhorn, “Weakly o-minimal structures and real closed fields,” Trans. Am. Math. Soc., 352, No. 12, 5435-5483 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  3. B. S. Baizhanov, “Expansion of a model of a weakly o-minimal theory by a family of unary predicates,” J. Symb. Log., 66, No. 3, 1382-1414 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Sh. Kulpeshov, “The convexity rank and orthogonality in weakly o-minimal theories,” Izv. NAN RK, Ser. Fiz.-Mat., No. 227, 26-31 (2003).

    MathSciNet  Google Scholar 

  5. B. Sh. Kulpeshov, “Countably categorical quite o-minimal theories,” Vestnik NGU, Mat., Mekh., Inf., 11, No. 1, 45-57 (2011).

    MATH  Google Scholar 

  6. L. L. Mayer, “Vaught’s conjecture for o-minimal theories,” J. Symb. Log., 53, No. 1, 146-159 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Sh. Kulpeshov, “Weakly o-minimal structures and some of their properties,” J. Symb. Log., 63, No. 4, 1511-1528 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  8. B. Sh. Kulpeshov and S. V. Sudoplatov, “Vaught’s conjecture for quite o-minimal theories,” Ann. Pure Appl. Log., 168, No. 1, 129-149 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  9. S. V. Sudoplatov, Classification of Countable Models of Complete Theories, Novosibirsk, Novosibirsk State Tech. Univ. (2014).

    MATH  Google Scholar 

  10. I. V. Shulepov and S. V. Sudoplatov, “Algebras of distributions for isolating formulas of a complete theory,” Sib. El. Mat. Izv., 11, 380-407 (2014); http://semr.math.nsc.ru/v11/p380-407.pdf.

    MathSciNet  MATH  Google Scholar 

  11. K. A. Baikalova, D. Yu. Emel’yanov, B. Sh. Kulpeshov, E. A. Palyutin, and S. V. Sudoplatov, “On algebras of distributions of binary isolating formulas for theories of Abelian groups and their ordered enrichments,” Izv. Vyssh. Uch. Zav., Mat., No. 4, 3-15 (2018).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630073, Russia

    D. Yu. Emel’yanov

  2. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science RK, ul. Pushkina 125, Alma-Ata, Kazakhstan, 050010

    D. Yu. Emel’yanov

  3. International Information Technologies University, Manas str. 34/1, Alma-Ata, Kazakhstan, 050040

    B. Sh. Kulpeshov

  4. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science RK, ul. Pushkina 125, Alma-Ata, Kazakhstan, 050010

    B. Sh. Kulpeshov

  5. Kazkh-British Technical University, ul. Tole bi 59, Alma-Ata, Kazakhstan, 050000

    B. Sh. Kulpeshov

  6. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    S. V. Sudoplatov

  7. Novosibirsk State Technical University, pr. Marksa 20, Novosibirsk, 630073, Russia

    S. V. Sudoplatov

  8. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    S. V. Sudoplatov

  9. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science RK, ul. Pushkina 125, Alma-Ata, Kazakhstan, 050010

    S. V. Sudoplatov

Authors
  1. D. Yu. Emel’yanov
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  2. B. Sh. Kulpeshov
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  3. S. V. Sudoplatov
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Corresponding author

Correspondence to D. Yu. Emel’yanov.

Additional information

Supported by RFBR (project No. 17-01-00531-a), by KN MON RK (project No. AP05132546), and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002).

Translated from Algebra i Logika, Vol. 57, No. 6, pp. 662-683, November-December, 2018.

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Emel’yanov, D.Y., Kulpeshov, B.S. & Sudoplatov, S.V. Algebras of Distributions of Binary Isolating Formulas for Quite o-Minimal Theories. Algebra Logic 57, 429–444 (2019). https://doi.org/10.1007/s10469-019-09515-5

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  • DOI: https://doi.org/10.1007/s10469-019-09515-5

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