The Goodstein principle is a natural number-theoretic theorem which is unprovable in Peano arithmetic. Since the original process definition there have been different canonical representation using Fast-Growing hierarchies. These representations give a natural Goodstein process independent from theories of various strength. In this talk we consider a normal forms based on Bachmann-Howard Hardy hierarchy from which we obtain a Goodstein process independent from the theory of ID2.
This is joint work with A. Weiermann on exploring normal form notations for the Goodstein principle.