Algebras of distributions of binary semi-isolating formulas for families of isolated types and for countably categorical theories

TL;DR

This paper develops a general framework for analyzing distributions of binary semi-isolating formulas within families of isolated types and countably categorical theories, enhancing understanding of their algebraic structures.

Contribution

It introduces a novel approach for studying distributions of semi-isolating formulas in specific classes of theories, expanding the algebraic analysis of isolated types.

Findings

Framework applicable to families of isolated types

Extension to countably categorical theories

Improved understanding of algebraic structures in these theories

Abstract

We apply a general approach for distributions of binary isolating and semi-isolating formulas to families of isolated types and to the class of countably categorical theories.