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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 45

Algebras of Binary Isolating Formulas for Strong Product Theories

Author(s)
Dmitry Yu. Emel’yanov1

1Novosibirsk State Technical University, Novosibirsk, Russian Federation

Abstract
Algebras of distributions of binary isolating and semi-isolating formulas are objects that are derived for a given theory, and they specify the relations between binary formulas of the theory. These algebras are useful for classifying theories and determining which algebras correspond to which theories. In the paper, we discuss algebras of binary formulas for strong products and provide Cayley tables for these algebras. On the basis of constructed tables we formulate a theorem describing all algebras of distributions of binary formulas for the theories of strong multiplications of regular polygons on an edge. In addition, we shows that these algebras can be absorbed by simplex algebras, which simplify the study of that theory and connect it with other algebraic structures. This concept is a useful tool for understanding the relationships between binary formulas of a theory.
About the Authors
Dmitry Yu. Emelyanov, Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation, dima-pavlyk@mail.ru
For citation
Emel’yanov D. Yu. Algebras of Binary Isolating Formulas for Strong Product Theories. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 45, pp. 138–144. https://doi.org/10.26516/1997-7670.2023.45.138
Keywords
algebra of binary isolating formulas, strong product, model theory, Cayley tables
UDC
510.67
MSC
03C07, 03C60
DOI
https://doi.org/10.26516/1997-7670.2023.45.138
References
  1. Emel’yanov D.Yu. On the algebra distributions of binary formulas of unary theories. The Bulletin of Irkutsk State University. Series Mathematics, 2016, vol. 17, pp. 23–36.
  2. Emelyanov D.Y. Algebras of binary isolating formulas for simplex theories.Algebra and Model Theory 11. Collection of papers, Novosibirsk, NSTU Publ., 2017, pp. 66–74.
  3. Emel’yanov D.Yu. Algebras of binary isolating formulas for theories of Cartesian products of graphs. Algebra and model theory 12. Collection of papers. Novosibirsk, NSTU Publ., 2019, pp. 21–31.
  4. Emelyanov D.Yu. Algebra distributions of binary formulas for theories of Archimedean bodies. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 28, pp. 36–52. https://doi.org/10.26516/1997-7670.2019.28.36
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  9. Sudoplatov S.V. Hypergraphs of prime models and distributions of countable models of small theories. J. Math. Sciences, 2010, vol. 169, no. 5, pp. 680–695. https://doi.org/10.1007/s10958-010-0069-9
  10. Sudoplatov S.V. Algebras of distributions for semi-isolating formulas of a complete theory. Siberian Electronic Mathematical Reports, 2014, vol. 11, pp. 408–433.
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