Algebras of Binary Isolating Formulas for Theories of Root Products of Graphs

• Main Author: D.Yu. Emel’yanov
• Format: Article
• Language: English
• Published: Irkutsk State University 2021-09-01
• Series: Известия Иркутского государственного университета: Серия "Математика"
• Subjects: algebra of binary isolating formulas; root product of graphs
• Online Access: http://mathizv.isu.ru/en/article/file?id=1387

Algebras of distributions of binary isolating and semi-isolating formulas are derived objects for given theory and reflect binary formula relations between realizations of 1-types. These algebras are associated with the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to the theories from this class and classify these algebras; 2) to classify theories from a given class depending on the algebras defined by these theories of isolating and semi-isolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semi-isolating formulas, which makes it possible to track the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulae for root products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems describing all algebras of binary formulae distributions for the root multiplication theory of regular polygons on an edge are formulated. It is shown that they are completely described by two algebras.