# The Additive Structure of Integers with the Lower Wythoff Sequence

## TL;DR

This paper proves the decidability of the additive structure of integers combined with a function related to the golden ratio using a pure model-theoretic approach.

## Contribution

It introduces a novel model-theoretic proof for the decidability of a specific integer structure involving the lower Wythoff sequence and the golden ratio.

## Key findings

- Decidability of the additive structure with the function f.
- Pure model-theoretic proof technique.
- Connection to the lower Wythoff sequence.

## Abstract

We have provided a pure model-theoretic proof for the decidability of the additive structure of the integers together with the function {f} sending {x} to {[\phi x]} where {\phi} is the golden ratio.