On relative separability in hypergraphs of models of theories

TL;DR

This paper introduces and explores the concept of relative separability in hypergraphs of models of theories, providing characterizations and applications, especially in ordered theories like o-minimal theories.

Contribution

It defines notions of relative separability for hypergraphs of models and characterizes these notions in general and for specific ordered theories.

Findings

Characterizations of relative separability in general theories

Specific characterizations for almost countably categorical o-minimal theories

Applications to ordered theories

Abstract

In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general case and for almost countably categorical quite o-minimal theories are established.