Recursive functionals and quantifiers of finite types. I
S. C. Kleene · Transactions of the American Mathematical Society · 1959
This result was obtained by Tarski [28], using set variables.Also cf.[29].(2) Cf.XXXIX below.This paper incorporates (with a new method of proof) the results alluded to in the last sentence of the abstract of [14] as presented to the Association for Symbolic Logic on December 29, 1952 (J.Symb.Logic vol.18 (1953) p. 190), and is the paper referred to in [14, p. 312] and [16, p. 212] as to be written under the title Analytic predicates and function quantifiers of higher finite types.The term "analytic" was applied in [14] to the predicates obtained by quantifying variables of types gl, and we have meanwhile decided that it would invite confusion to extend the use of "analytic" to include quantification of highertype variables; hence the present change of title.1