On resemblance and recursive isomorphism types of bounded partial recursive functions (Q1577169)

Partial recursive functions \(\alpha\) and \(\beta\) are called resembling provided there exist recursive permutations \(f\) and \(g\) such that \(\alpha=f^{-1}\beta g\); they are called recursively isomorphic if there exists a recursive permutation \(f\) such that \(\alpha=f^{-1}\beta f\). A function is called bounded if its range is bounded. The author proves that each resemblance type of a bounded function consists of finitely many recursive isomorphism types; an upper bound is presented for the number of recursive isomorphism types in the resemblance type of a bounded function; for some bounded functions, the exact number of recursive isomorphism types is determined.