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  1. A computable ordinary differential equation which possesses no computable solution.Marian Boylan Pour-el - 1979 - Annals of Mathematical Logic 17 (1):61.
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  • Computability of boolean algebras and their extensions.Donald A. Alton & E. W. Madison - 1973 - Annals of Mathematical Logic 6 (2):95-128.
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  • When series of computable functions with varying domains are computable.Iraj Kalantari & Larry Welch - 2013 - Mathematical Logic Quarterly 59 (6):471-493.
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  • The broad conception of computation.Jack Copeland - 1997 - American Behavioral Scientist 40 (6):690-716.
    A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by (...)
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  • Computability of Self‐Similar Sets.Hiroyasu Kamo & Kiko Kawamura - 1999 - Mathematical Logic Quarterly 45 (1):23-30.
    We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar set is a recursive compact set. A further result on the case that the self-similar set forms a curve is also discussed.
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  • Real numbers, continued fractions and complexity classes.Salah Labhalla & Henri Lombardi - 1990 - Annals of Pure and Applied Logic 50 (1):1-28.
    We study some representations of real numbers. We compare these representations, on the one hand from the viewpoint of recursive functionals, and of complexity on the other hand.The impossibility of obtaining some functions as recursive functionals is, in general, easy. This impossibility may often be explicited in terms of complexity: - existence of a sequence of low complexity whose image is not a recursive sequence, - existence of objects of low complexity but whose images have arbitrarily high time- complexity .Moreover, (...)
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  • 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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  • Beyond the universal Turing machine.Jack Copeland - 1999 - Australasian Journal of Philosophy 77 (1):46-67.
    We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of well-defined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
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  • Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. I.Iraj Kalantari & Lawrence Welch - 1998 - Annals of Pure and Applied Logic 93 (1-3):125-151.
    In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In the succeeding (...)
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