1. Aczel,P. 1970 Representability in some systems of second-order arithmetic, Israel Jour.Math. (1970) 309–328. (Studies the relationship between recursion in E # 1 , Σ 1 1 inductive definability, and representability in a certain formal axiomatic system for arithmetic).
2. Aczel,P. and Hinman,P. 1974 Recursion in the superjump, in Fenstad-Hinman [1974],3–41 (This paper shows that the jump hierarchy fails to exhaust 2-sc(II) whenever the superjump functional is recursive in II and constructs a more elaborate jump hierarchy which does exhaust 2-sc (sπ). The connections between recursion in type-2 functionals and ordinal recursion are explored in some detail and include Theorem J (i).)
3. Barwise, K.J. 1977 Handbook of Mathematical Logic, North Holland, Amsterdam 1976.
4. Bergstra, I. 1976 Computability and Continuity in Finite Types, Ph.D. Thesis, University of Utrecht, Netherland, 1976,184 pp. (A good introduction to the theory of continuous and countable functionals, which contains in addition to new results a survey of many older ones).
5. Crossley, J.N. 1967 Sets, Models, and Recursion Theory (Proceedings of the Summer School in Mathematical Logic and Logic Colloquium, Leicester, England, 1965, Editor) North Holland, Amsterdam, 1967, 331 pp.