From A1 to D5: Towards a Forcing-Related Classification of Relational Structures

TL;DR

This paper explores the classification of countable binary relational structures based on the properties of their associated posets of isomorphic substructure domains, linking to forcing-related concepts in set theory.

Contribution

It introduces a forcing-related classification framework for relational structures, focusing on the partial orderings of their isomorphic substructure domains.

Findings

Provides a rough classification of countable binary structures

Connects the properties of these structures to forcing concepts

Analyzes the partial orderings of substructure domains

Abstract

We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the forcing-related properties of the posets of their copies is obtained.