VARIATIONS ON A THEME BY WEIERMANN

Weiermann [18] introduces a new method to generate fast growing functi ons in order to get an elegant and perspicuous proof of a bounding the orem for provably total recursive functions in a formal theory, e.g., in PA. His fast growing function Born is described as follows. For eac h ordinal alpha and natural number n let T-n(alpha) denote a finitely branching, primitive recursive tree of ordinals, i.e., an ordinal as a label is attached to each node in the tree so that the labelling is c ompatible with the tree ordering. Then the tree T-n(alpha) is well fou nded and hence finite by Konig's lemma. Define theta alpha n = the dep th of the tree T-n(alpha)=the length of the longest branch in T-n(alph a). We introduce new fast and slow growing functions in this mode of d efinitions and show that each of these majorizes provably total recurs ive functions in PA.