ABSTRACT
In this chapter we return to Goodstein’s theorem, the result proved in Chapter 2 with the help of ε0-induction. We find a natural generalization of Goodstein’s theorem that is not only a consequence of ε0-induction, but also equivalent to it. It follows that the generalized Goodstein theorem implies the consistency of PA, and hence it is not provable in PA. This gives us our first example of a natural theorem not provable in PA.
