  In the article 'Ordinal Logics and the Characterizations of the Informal
Concept of Proof', Georg Kreisel poses the problem of assigning unique
notations to recursive ordinals, and additionally suggests that the methods
which are developed for its solution will be non-constructive in character. In
this paper we develop methods in which various uniqueness results for notations
of recursive ordinals can be obtained, and thereafter apply these results to
investigate the problems surrounding the hierarchical classification of the
computable functions.
