Appendix A: Gödel’s Theorems
Hilbert’s program was formulated by the mathematician David Hilbert in the early twentieth century. The main goal of this program was to establish the foundations for all mathematics, that is, to define all of mathematics in a single formal system. In other words, the program sought to find a formal system from which one could deduce all possible truths about mathematics. In this appendix, we will show the mathematical answer that was found to address this program.
Definition 1 Gödel numbering is a function that assigns a natural number to each symbol or well-formed formula in a formal system.
For example, within Peano’s ...