Algebras of Binary Isolating Formulas for Tensor Product Theories

Abstract

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

Keywords

• algebra of binary isolating formulas
• tensor product
• model theory
• cayley tables