Abstract

In this undergraduate thesis the independence of Goodstein's Theorem from Peano arithmetic (PA) is proved, following the format of the rst proof, by Kirby and Paris. All the material necessary for its understanding is developed, beginning with the foundations of set theory, followed by ordinal numbers and a proof of Goodstein's Theorem, and concluded with basic model theory and the independence proof. Other relevant information, such as an outline for an alternative independence proof and an application to dynamical systems is also included. Contents 1.