Goldbach's Conjecture — Towards the Inconsistency of Arithmetic

This paper proves, using methods from elementary number theory, that there is an inconsistency in Peano arithmetic (PA), where the centerpiece is a strengthened form of the strong Goldbach conjecture. We express this form of the conjecture in terms of an infinite set and show that the conjunction of two properties of this set leads to a contradiction. An essential point here is the constructive role of the prime numbers within the natural numbers.