Algebraic and logical methods in computer science and artificial intelligence

Algebras of binary isolating formulas for homomorphic product theories

D. Yu. Emelyanov

Novosibirsk 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.

Keywords: algebra of binary isolating formulas, homomorphic product, model theory, Cayley tables.

UDC: 510.67

MSC: 03C07, 03C60

Received: 09.07.2024
Revised: 08.11.2024
Accepted: 11.11.2024

Language: English

DOI: 10.26516/1997-7670.2025.52.153