The counting hierarchy in binary notation (Q1008842)

Summary: We present a new recursion-theoretic characterization of FCH, the hierarchy of counting functions, in binary notation. Afterwards we introduce a theory of bounded arithmetic, TCA, that can be seen as a reformulation, in the binary setting, of Jan Johannsen and Chris Pollett's system \(D^{0}_{2}\). Using the previous inductive characterization of FCH, we show that a strategy similar to the one applied to \(D^{0}_{2}\) can be used in order to characterize FCH as the class of functions provably total in TCA.