Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Computable analysis: an introduction
Computable analysis: an introduction
Characterization of the Computable Real Numbers by Means of Primitive Recursive Functions
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Characterization of the Computable Real Numbers by Means of Primitive Recursive Functions
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Primitive Recursiveness of Real Numbers under Different Representations
Electronic Notes in Theoretical Computer Science (ENTCS)
Representation of left-computable ε-random reals
Journal of Computer and System Sciences
Complexity and intensionality in a type-1 framework for computable analysis
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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One usually defines the notion of a computable real number by using recursive functions. However, there is a simple way due to A. Mostowski to characterize the computable real numbers by using only primitive recursive functions.We prove Mostowski's result differently and apply it to get other simple characterizations of this kind. For instance, a real number is shown to be computable if and only if it belongs to all members of some primitive recursive sequence of nested intervals with rational end points and with lengths arbitrarily closely approaching 0.