Goldbach's Conjecture — Towards the Inconsistency of Arithmetic

Abstract

This paper proves that ZFC and Peano arithmetic (PA) are inconsistent, the latter result being a corollary of the former. We introduce a metatheory over ZFC that allows us to use statements in the proof that express logical consequence. We then show, by explicitly stating a contradiction, that this metatheory is inconsistent, which immediately leads to the inconsistency of ZFC. The contradiction itself is triggered by the conjunction of two properties of an infinite set, with which we express a strengthened form of the strong Goldbach conjecture. We use elementary number theory, where the constructive role of prime numbers within the natural numbers is a key point.