Goldbach's Conjecture — A Route to the Inconsistency of Arithmetic

This paper proves an inconsistency in Peano arithmetic (PA). For a strengthened form of the strong Goldbach conjecture and its negation, the paper proves that we have a proof of either the conjecture or its negation, when in fact we have no proof for either. In other words, the paper actually does not solve the conjecture, but it proves that it does. This contradiction is the consequence of two properties of a specific set which we use to reformulate the conjecture.