Constructibility and the P versus NP problem
Computational Complexity
2026-05-26 v7 Logic in Computer Science
Abstract
The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain natural conditions, then no constructible, arithmetically sound and formalizable theory proves P = NP.
Keywords
Cite
@article{arxiv.2406.16843,
title = {Constructibility and the P versus NP problem},
author = {Arne Hole},
journal= {arXiv preprint arXiv:2406.16843},
year = {2026}
}
Comments
10 pages, no figures. Compared to previous versions, the paper is substantially rewritten. It now focuses on the P versus NP problem only, giving a complete proof of the main result concerning that problem