\(\Gamma_0\) may be minimal subrecursively inaccessible (Q2743650)

The author demonstrates that \(\Gamma_0\) can be a subrecursively inaccessible ordinal. He first modifies the definition of fundamental sequences (to limit ordinals), and then shows that the fast- and slow-growing hierarchies based on these sequences match up for the first time at \(\Gamma_0\), which is the definition of subrecursive inaccessibility. He, further, gives two Grzegorczyk-type hierarchies up to \(\Gamma_0\) that both classify the \(<\Gamma_0\)-recursive functions. One hierarchy is based on the new fundamental sequences, and the other on those used by \textit{S. Feferman} [J. Symb. Log. 33, 193-220 (1968; Zbl 0162.02201)]. The author gives a clear presentation of basic ideas and directions, but the details need an awful amount of symbols, case distinctions, etc., due to the nature of the subject.