Is the twin prime conjecture independent of Peano Arithmetic?
Logic
2021-11-03 v3
Abstract
We show that there is an arithmetical formula F such that ZF proves that F is independent of PA and yet, unlike other arithmetical independent statements, the truth value of F cannot at present be established in ZF or in any other trusted metatheory. In fact we can choose an example of such a formula F such that ZF proves that F is equivalent to the twin prime conjecture.
Keywords
Cite
@article{arxiv.2110.08640,
title = {Is the twin prime conjecture independent of Peano Arithmetic?},
author = {Alessandro Berarducci and Antongiulio Fornasiero and Joel David Hamkins},
journal= {arXiv preprint arXiv:2110.08640},
year = {2021}
}
Comments
4 pages. Added Hamkins as coauthor and a sharper version of the main result (Theorem 1)