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doi:10.1016/S0304-3975(00)00070-0 
Copyright © 2000 Elsevier Science B.V. All rights reserved.
Grzegorczyk's hierarchy of computable analysis*1
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Qing Zhou
Received 1 November 1997;
Abstract
This paper deals with the computability in analysis within the framework of Grzegorczyk's hierarchy, which is in the number 1 of addendum of open problems in Pour-El and Richards ([5], Computability in Analysis and Physics, Springer, Berlin, 1989). We combine two concepts, computability for sequences of real-valued functions and Grzegorczyk's hierarchy for recursive number theoretic functions, together and examine the computability in analysis restricted to primitive recursion and below. The notions of (
) primitive computability structures on Banach space, in particular, for sequences of reals and real-valued functions are introduced; relations between (
) primitive computability structures are proved; some basic properties are studied.
Author Keywords: (
) Primitively computable sequences of reals; (
) Primitively computable sequences of real-valued functions; (
) Primitive computability structures on Banach space
*1 Some of the results in this paper were announced in Cocoon’97 and published in the Lecture Notes in Computer Science no. 1276.
