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This is the third of a series of papers in these Transactions on hierarchies obtained by quantifying variables of recursive predicates. In Recursive predicates and quantifiers [10] variables for natural numbers (type 0) were quantified, and in Arithmetical predicates and function quantifiers [14] also variables for one-place number-theoretic functions (type(More)
For over two millenia mathematicians have used particular examples of algorithms for determining the values of functions. The notion of "?-definability" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of the functions for which algorithms exist. This article explains the notion and traces the investigation(More)