The Journal of Symbolic Logic

Research Article

Unary primitive recursive functions

Daniel E. Severin

Facultad de Ciencias Exactas, Ingenieria y Agrimensura, Universidad Nacional de Rosario, Rosario. Santa Fe, Argentina, URL:,


In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets.

(Received March 09 2006)

Key words and phrases

  • unary;
  • primitive recursive;
  • recursion scheme;
  • reduction