The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected...
The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at
any point is just the value of the first function in the sequence which is defined at that point.
In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a
hierarchy connected...
A modified version of the classical -operator as well as the
first value operator and the operator of inverting unary
functions, applied in combination with the composition of
functions and starting from the primitive recursive functions,
generate all arithmetically representable functions. Moreover, the
nesting levels of these operators are closely related to the
stratification of the arithmetical hierarchy. The same is shown
for some further function operators known from computability and complexity
theory....
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