Is the twin prime conjecture independent of Peano Arithmetic?

Alessandro Berarducci; Antongiulio Fornasiero; Joel David Hamkins

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arXiv · 2110.08640

Is the twin prime conjecture independent of Peano Arithmetic?

Alessandro Berarducci·Antongiulio Fornasiero·Joel David Hamkins

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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.

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BibTeX RIS

Alessandro Berarducci, Antongiulio Fornasiero, Joel David Hamkins. 2021-10-16. Is the twin prime conjecture independent of Peano Arithmetic?. https://arxiv.org/abs/2110.08640

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