# Definable families of theories, related calculi and ranks

## TL;DR

This paper explores definable subfamilies of theories, their calculi, and characteristics like rank and degree, providing a framework for understanding their structural properties.

## Contribution

It introduces a systematic study of sentence- and diagram-definable subfamilies of theories, along with calculi and dynamic characteristics related to rank and degree.

## Key findings

- Defined sentence- and diagram-definable subfamilies of theories
- Developed calculi for these subfamilies
- Analyzed their rank and degree characteristics

## Abstract

We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.