Extension of partial recursive functions and functions with a recursive graph

It is proved that every degree of complexity of mass problems, containing the decision problem of a recursive enumerable set, contains also the problem of extension of a partial recursive function, the graph of which is recursive. Some properties of functions with a recursive graph are considered.Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 261–267, February, 1969.The author is deeply indebted to V. A. Uspenskii for discussion of the results.