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By A. I Arruda, N. C. A. da Costa, R. Chuaqui

ISBN-10: 0720407524

ISBN-13: 9780720407525

Shipped from united kingdom, please permit 10 to 21 company days for arrival. Nonclassical Logics version conception and Computability , hardcover, ex lib yellow binding pub by way of NorthHolland

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1937], “On Computable Numbers, With an Application to the Entscheidungsproblem”, Proceedings of London Mathematical Society, Series 2 42(1936–1937), 230–265; correction, ibidem 43, pp. 544–546. Reprinted in [Davis 1965, pp. asp>. A. [1992], “Kolmogorov and Mathematical Logic”, Journal of Symbolic Logic 57(2), 385–412. A. L. [1993], “Algorithms: Main Ideas and Applications”, Kluwer. 57 Douglas S. D. thesis [Brouwer 1907]) and Markov’s recursive constructive mathematics (RUSS) [Markov]. The first of these introduced to mathematics Brouwer’s continuity principle—a feature that renders intuitionistic and classical mathematics (CLASS) superficially contradictory but, in reality, barely comparable—and his Fan Theorem, which predated the appearance of its contrapositive, K¨onig’s Lemma, in classical mathematics.

5. Formalization of Sequential Algorithms Is it possible to capture (=formalize) sequential algorithms on their natural levels of abstraction? Furthermore, is there one machine model that captures all sequential algorithms on their natural levels of abstraction? According to [Gurevich 2000], the answer to both questions is yes. We outline the approach of [Gurevich 2000] and put forward a slight but useful generalization. 40 Andreas Blass, Yuri Gurevich As a running example of a sequential algorithm, we use a version Euc of Euclid’s algorithm that, given two natural numbers, computes their greatest common divisor d.

E. [1981], The Art of Computer Programming, vol. 2: Seminumerical Algorithms, Addison-Wesley, Reading, MA. N. [1953], “On the Concept of Algorithm”, Uspekhi Mat. Nauk 8(4), 175–176, Russian. An English translation is found in [Uspensky and Semenov 1993, pp. 18–19]. N. A. [1958], “On the Definition of Algorithm”, Uspekhi Mat. Nauk 13(4), 3–28, Russian. Translated into English in AMS Translations 29(1963), 217–245. A. [1973], “Universal Search Problems”, Problemy Peredachi Informatsii 9(3), 265–266, Russian.

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Non-classical logics, model theory and computability: Proceedings Campinas, 1976 by A. I Arruda, N. C. A. da Costa, R. Chuaqui


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