# A Formal Axiomatization of Computation

## TL;DR

This paper presents an axiomatic framework for computation inspired by Brouwer choice sequences, constructing a model that demonstrates P does not equal NP within an intuitionistic viewpoint.

## Contribution

It introduces a formal axiomatization of computation and constructs a model satisfying P ≠ NP based on Brouwer's intuitionism.

## Key findings

- Constructs a model $E$ satisfying the axioms
- Shows $E
ot= P$ NP within the model
- Supports the view that P ≠ NP in an intuitionistic context

## Abstract

We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding "effective computability" in Brouwer intuitionism viewpoint, we show $\mathrm{ P \neq NP}$.