The Consequences of Gödel’s Incompleteness Theorems for the Consistency of Mathematics.

Abstract

The aim was to provide a clear overview of Gödel's Incompleteness Theorems. The thesis covers primitive recursive functions and relations, some properties of Peano Arithmetic (PA for short), and material required to prove that PA is incomplete and unable to prove its own consistency. Finally, the thesis considers some consequences of Gödel's work, one of which relates to Hilbert's Program.