Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
A Finite Hierarchy of the Recursively Enumerable Real Numbers
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Relatively Recursive Reals and Real Functions
Relatively Recursive Reals and Real Functions
Closure Properties of Real Number Classes under Limits and Computable Operators
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Densities and entropies in cellular automata
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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A real number is computable if it is the limit of an effectively converging computable sequence of rational numbers, and left (right) computable if it is the supremum (infimum) of a computable sequence of rational numbers. By applying the operations "sup" and "inf" alternately n times to computable (multiple) sequences of rational numbers we introduce a non-collapsing hierajchy {Σn,IIn,Δn : n Ɛ N} of real numbers. We characterize the classes Σ2,II2 and Δ2 in various ways and give several interesting examples.