Goldbach's Conjecture — Towards the Inconsistency of Arithmetic

This paper proves an inconsistency in Peano arithmetic (PA). We express a strengthened form of the strong Goldbach conjecture and its negation by using a specific set that varies according to whether the conjecture or the negation is assumed. We show that, on the other hand, this set remains unchanged under these assumptions. This causes a contradiction.First submission to the Annals of Mathematics on March 24, 201