Definability lattice for addition of rationals

TL;DR

This paper explores the structure of all possible reducts of the rational numbers with addition, analyzing their relationships within a lattice framework to understand their definability properties.

Contribution

It introduces a detailed lattice structure for the reducts of (Q, +), providing new insights into their definability and classification.

Findings

Identifies the lattice of reducts of (Q, +)

Classifies the definability relations among reducts

Provides a comprehensive structure for understanding reducts of rational addition

Abstract

In the present paper we discuss the lattice of reducts of $\langle \mathbb{Q}, \{$+$\} \rangle$