Expansions and restrictions of structures and theories, their hierarchies

TL;DR

This paper explores the hierarchical properties of expansions and restrictions of structures and theories, applying the approach to various classes including ω-categorical, Ehrenfeucht, strongly minimal, ω₁-theories, and stable theories.

Contribution

It introduces general principles and hierarchical properties for expansions and restrictions, providing a unified framework for diverse classes of theories and structures.

Findings

Describes hierarchical properties for ω-categorical theories

Analyzes expansions and restrictions in Ehrenfeucht theories

Applies principles to strongly minimal and ω₁-theories

Abstract

We introduce and study some general principles and hierarchical properties of expansions and restrictions of structures and their theories The general approach is applied to describe these properties for classes of $\omega$-categorical theories and structures, Ehrenfeucht theories and their models, strongly minimal, $\omega_1$-theories, and stable ones.