Abstract

Let T be the standard Veblen 1908 ordinal notation system for Γ0 as defined, for example, in Schütte's 1977 textbook [13] on Proof Theory. We define a slight modification of the standard assignment of fundamental sequences for the limit ordinals in T and prove that Γ0 is subrecursively inaccessible for this assignment, i.e. the induced slow and fast growing hierarchy match up at Γ0 for the first time.The results of this paper also indicate that φε00 may be considered as a new slow growing ordinal of PA in the sense that the induced slow growing hierarchy up to φε00 classifies the PA-provablyrecursive functions.We show how the results of this paper can be used to bui d a subrecursive hierarchyover the predicative ordinals in the spirit of Wainer's 1970 abstract [16 ]