For any function h:N → N, we call a real number x h-bounded computable (h-bc for short) if there is a computable sequence (x_s) of rational numbers which converges to x such that, for any n ∈ N, there are at most h(n) pairs of non-overlapped indices (i,j) with |x_i - x_j| ≥ 2~(-n). In this paper we investigate h-bc real numbers for various functions h. We will show a simple sufficient condition for class of functions such that the corresponding h-bc real numbers form a field. Then we prove a hierarchy theorem for h-bc real numbers. Besides we compare the semi-computability and weak computability with the h-bounded computability for special functions h.
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机译：对于任何功能H：n→n，如果有可计算的序列（x_s），则呼叫实数x H型可计算（H-BC for Short），如果有合理的数量，则会收敛到x，使得任何n∈n ，最多有h（n）对的非重叠索引（i，j）与| xi-x_j | ≥2〜（-N）。在本文中，我们研究了各种功能H的H-BC实数。我们将为功能类显示一个简单的足够条件，以使相应的H-BC实数形成一个字段。然后我们证明了H-BC实数的层次结构定理。除了我们比较半可计算性和弱的可计算性，对特殊功能H的H型界可计算性H。
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