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  1.  5
    Monotonically Computable Real Numbers.Robert Rettinger, Xizhong Zheng, Romain Gengler & Burchard von Braunmühl - 2002 - Mathematical Logic Quarterly 48 (3):459-479.
    Area number x is called k-monotonically computable , for constant k > 0, if there is a computable sequence n ∈ ℕ of rational numbers which converges to x such that the convergence is k-monotonic in the sense that k · |x — xn| ≥ |x — xm| for any m > n and x is monotonically computable if it is k-mc for some k > 0. x is weakly computable if there is a computable sequence s ∈ ℕ of (...)
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  2.  41
    H‐Monotonically Computable Real Numbers.Xizhong Zheng, Robert Rettinger & George Barmpalias - 2005 - Mathematical Logic Quarterly 51 (2):157-170.
    Let h : ℕ → ℚ be a computable function. A real number x is called h-monotonically computable if there is a computable sequence of rational numbers which converges to x h-monotonically in the sense that h|x – xn| ≥ |x – xm| for all n andm > n. In this paper we investigate classes h-MC of h-mc real numbers for different computable functions h. Especially, for computable functions h : ℕ → ℚ, we show that the class h-MC coincides (...)
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  3.  17
    Weak Computability and Representation of Reals.Xizhong Zheng & Robert Rettinger - 2004 - Mathematical Logic Quarterly 50 (45):431-442.
    The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the primitive recursiveness and polynomial time computability of the reals do depend on the representation. In this paper, we explore how (...)
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  4.  2
    Compactness and the Effectivity of Uniformization.Robert Rettinger - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 616--625.
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