Weakly computable real numbers
Journal of Complexity
On the divergence bounded computable real numbers
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
On the turing degrees of divergence bounded computable reals
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Finitely Bounded Effective Computability
Electronic Notes in Theoretical Computer Science (ENTCS)
A Hierarchy of Computably Enumerable Reals
Fundamenta Informaticae
A Hierarchy of Computably Enumerable Reals
Fundamenta Informaticae
Bounded computable enumerability and hierarchy of computably enumerable reals
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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A real number x is f-bounded computable (f-bc, for short) for a function f if there is a computable sequence (x"s) of rational numbers which converges to x f-bounded effectively in the sense that, for any natural number n, the sequence (x"s) has at most f(n) non-overlapping jumps of size larger than 2^-^n. f-bc reals are called divergence bounded computable if f is computable. In this paper we give a hierarchy theorem for Turing degrees of different classes of f-bc reals. More precisely, we will show that, for any computable functions f and g, if there exists a constant @c1 such that, for any constant c, f(n@c)+n+c=