Paper
The fractal Goodstein principle
Authors
David Fernández-Duque, Andreas Weiermann
Abstract
The original Goodstein process is based on writing numbers in hereditary -exponential normal form: that is, each number is written in some base as , with and iteratively being written in hereditary -exponential normal form. We define a new process which generalises the original by writing expressions in terms of a hierarchy of bases , instead of a single base . In particular, the `digit' may itself be written with respect to a smaller base . We show that this new process always terminates, but termination is independent of Kripke-Platek set theory, or other theories of Bachmann-Howard strength.