# Approximations of theories

## TL;DR

This paper investigates various methods of approximating logical theories, exploring their relationships with finitely axiomatizable theories, minimal generating sets, and their spectra, to better understand the structure and classification of theories.

## Contribution

It introduces new approximation techniques for theories and analyzes their connections with finitely axiomatizable theories and minimal generating sets.

## Key findings

- Identifies different types of theory approximations.
- Establishes links between approximations and finitely axiomatizable theories.
- Analyzes the concept of $e$-spectra in the context of theory approximations.

## Abstract

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of theories as well as their $e$-spectra are found.