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Russian Mathematics

, Volume 62, Issue 4, pp 1–12 | Cite as

On Algebras of Distributions of Binary Isolating Formulas for Theories of Abelian Groups and Their Ordered Enrichments

  • K. A. Baikalova
  • D. Yu. Emel’yanov
  • B. Sh. Kulpeshov
  • E. A. Palyutin
  • S. V. Sudoplatov
Article
  • 15 Downloads

Abstract

We describe algebras of distributions of binary isolating formulas for theories of abelian groups and some of their ordered enrichments. The base of this description is the general theory of algebras of isolating formulas. We also take into account the specificity of the basedness of theories of abelian groups on Szmielew invariants. We give Cayley tables for algebras that correspond to theories of basic abelian groups and their ordered enrichments and propose a technique for transforming algebras for theories of basic abelian groups into algebras for arbitrary theories of abelian groups.

Keywords

algebra of distributions of binary isolating formulas abelian group elementary theory ordered enrichment 

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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • K. A. Baikalova
    • 1
  • D. Yu. Emel’yanov
    • 2
  • B. Sh. Kulpeshov
    • 3
    • 4
  • E. A. Palyutin
    • 2
    • 4
    • 5
  • S. V. Sudoplatov
    • 1
    • 2
    • 4
    • 5
  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.International Information Technology UniversityAlmatyRepublic of Kazakhstan
  4. 4.Institute of Mathematics and Mathematical ModelingAlmatyRepublic of Kazakhstan
  5. 5.Sobolev Institute of Mathematics SB RASNovosibirskRussia

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