V. A. Uspensky, the extended version of this paper was published as a book: V.A. Uspensky, Gödel's Incompleteness Theorem, Theoretical Computer Science, vol.29, pp.239-319, 1974.

H. Rogers, Theory of Recursive Functions and Effective Computability, vol.10, 1967.

, One can also prove easily that axioms 1 and 3 alone describe the classes that are partial recursive closures of arbitrary functions. This means that (1) if f is some function, that the minimal class of functions that is closed under substitution, recursion, minimization and contains all partial recursive functions and f , satisfies axioms 1 and 3; (2) all classes that satisfy these two axioms can be