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Algebra and Logic

, Volume 57, Issue 6, pp 429–444 | Cite as

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

  • D. Yu. Emel’yanovEmail author
  • B. Sh. Kulpeshov
  • S. V. Sudoplatov
Article
  • 3 Downloads

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.

Keywords

quite o-minimal theory countable model convexity rank algebras of distributions of binary isolating formulas generalized commutative monoid 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • D. Yu. Emel’yanov
    • 1
    • 2
    Email author
  • B. Sh. Kulpeshov
    • 3
    • 4
    • 5
  • S. V. Sudoplatov
    • 6
    • 7
    • 8
    • 9
  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Institute of Mathematics and Mathematical ModelingMinistry of Education and Science RKAlma-AtaKazakhstan
  3. 3.International Information Technologies UniversityAlma-AtaKazakhstan
  4. 4.Institute of Mathematics and Mathematical ModelingMinistry of Education and Science RKAlma-AtaKazakhstan
  5. 5.Kazkh-British Technical UniversityAlma-AtaKazakhstan
  6. 6.Sobolev Institute of MathematicsNovosibirskRussia
  7. 7.Novosibirsk State Technical UniversityNovosibirskRussia
  8. 8.Novosibirsk State UniversityNovosibirskRussia
  9. 9.Institute of Mathematics and Mathematical ModelingMinistry of Education and Science RKAlma-AtaKazakhstan

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