Monotonically Computable Real Numbers

Mathematical Logic Quarterly 48 (3):459-479 (2002)
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Abstract

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 rational numbers converging to x such that the sum equation image|xs — xs + 1| is finite. In this paper we show that a mc real numbers are weakly computable but the converse fails. Furthermore, we show also an infinite hierarchy of mc real numbers

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Citations of this work

H‐monotonically computable real numbers.Xizhong Zheng, Robert Rettinger & George Barmpalias - 2005 - Mathematical Logic Quarterly 51 (2):157-170.
Approximation Representations for Δ2 Reals.George Barmpalias - 2004 - Archive for Mathematical Logic 43 (8):947-964.

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References found in this work

Nicht konstruktiv beweisbare sätze der analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Rekursive Funktionen.Raphael M. Robinson & Rozsa Peter - 1951 - Journal of Symbolic Logic 16 (4):280.

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