Goldbach's Conjecture — Towards the Inconsistency of Arithmetic

This paper proves that ZFC and Peano arithmetic (PA) are inconsistent, the latter result being a corollary of the former. We introduce a strengthened form of the strong Goldbach conjecture and show that both the conjecture and its negation can be deduced. The contradiction is triggered by the conjunction of two properties of an infinite set, which we use to reformulate the conjecture. We apply elementary number theory, where the constructive role of prime numbers within the natural numbers is a key point.