This article demonstrates the invalidity of Theorem VI in Gödel’s 1931, showing that propositions (15) and (16), derived from the definition 8.1, in its proof, are false in PA. Introduction. Developed as a consequence of the crisis of the foundation of mathematics due to the discovery of the antinomies, Hilbert’s formalism planned as criterions of adequacy for the axiomatic systems, the achieve...

The Extensible Messaging and Presence Protocol (XMPP) is an application profile of the Extensible Markup Language (XML) that enables the near-real-time exchange of structured yet extensible data between any two or more network entities. This document defines XMPP’s core protocol methods: setup and teardown of XML streams, channel encryption, authentication, error handling, and communication pri...