Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
Complexity theory of real functions
Complexity theory of real functions
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Computable analysis: an introduction
Computable analysis: an introduction
A Finite Hierarchy of the Recursively Enumerable Real Numbers
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The Arithmetical Hierarchy of Real Numbers
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Binary enumerability of real numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Weakly Computable Real Numbers and Total Computable Real Functions
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
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In effective analysis, various classes of real numbers are discussed. For example, the classes of computable, semi-computable, weakly computable, recursively approximable real numbers, etc. All these classes correspond to some kind of (weak) computability of the real numbers. In this paper we discuss mathematical closure properties of these classes under the limit, effective limit and computable function. Among others, we show that the class of weakly computable real numbers is not closed under effective limit and partial computable functions while the class of recursively approximable real numbers is closed under effective limit and partial computable functions.