An alternative proof of Godel's first incompleteness theorem

TL;DR

This paper presents a new proof of Godel's first incompleteness theorem that avoids the need for omega-consistency and does not rely on coding negated sentences, starting from the end of the traditional proof.

Contribution

It introduces an alternative proof method for Godel's first incompleteness theorem that simplifies assumptions and approach.

Findings

The proof does not require omega-consistency.

It avoids coding negated sentences as in Rosser's proof.

It provides a different starting point from the traditional proof.

Abstract

This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.