A proof of Liouville's theorem via o-minimality

TL;DR

This paper presents a novel proof of Liouville's theorem, demonstrating that every bounded entire complex function is constant, using the framework of o-minimality introduced by Peterzil and Starchenko.

Contribution

It introduces an o-minimality-based approach to prove a classical complex analysis result, offering a new perspective and methodology.

Findings

Proof of Liouville's theorem via o-minimality

Establishes a connection between model theory and complex analysis

Provides a concise alternative proof using o-minimal structures

Abstract

In this short note we give a proof of Liouville's theorem (every bounded entire complex function is constant) following Peterzil and Starchenko's approach to complex analysis via o-minimality.