Constructivity and Computability in Historical and by Jacques Dubucs, Michel Bourdeau

Machine Theory

By Jacques Dubucs, Michel Bourdeau

Preface; Jacques Dubucs and Michel Bourdeau.- bankruptcy 1. confident Recursive capabilities, Church's Thesis, and Brouwer's conception of the growing topic: Afterthoughts on a Parisian Joint consultation; Goran Sundholm.- bankruptcy 2. The advancements of the concept that of computing device computability from 1936 to the Sixties; Jean Mosconi.- bankruptcy three. Kolmogorov Complexity in viewpoint, half I: details concept and Randomness; Marie Ferbus-Zanda and Serge Grigorieff.- bankruptcy four. Kolmogorov Complexity in point of view, half II: type, details Processing and Duality; Marie Ferbus-Zanda.- bankruptcy five. Proof-theoretic semantics and feasibility; Jean Fichot.- bankruptcy 6. Recursive features and confident arithmetic; Thierry Coquand.- bankruptcy 7. Godel and intuitionism; Mark van Atten.

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J. von Neumann in his 1948 and 1949 suggested developing a “general and logical theory of automata” which could contribute to handling the problems of self-reproduction by using ideas particularly inspired by the universal Turing machine (von Neumann 1952–1953). In the book edited in 1956 by Shannon and J. McCarthy, Automata Studies, finite automata are clearly contrasted with infinite automata, namely Turing machines. Kleene, in his fundamental paper on finite automata (Kleene 1956, published in this book, but written in 1951), explicitly states that a Turing machine can be considered as a finite automaton supplied with an external, unbounded memory.

1970a). Church’s thesis: A kind of reducibility axiom for constructive mathematics. In A. Kino, J. Myhill, & R. E. ), Intuitionism and proof theory. Proceedings of the summer conference, Buffalo, 1968 (pp. 121–150). Amsterdam: North-Holland. Kreisel, G. (1970b). Review of Myhill (1967). Zentralblatt für Mathematik und ihre Grenzgebiete, 187, 263–265. Kreisel, G. (1971). Review of Kreisel (1970). Zentralblatt für Mathematik und ihre Grenzgebiete, 199, 300–301. Kreisel, G. (1987). Church’s thesis and the ideal of informal rigour.

Logique et intuitionnisme. In Actes du 2e colloque internationale de logique mathématique, Paris, 1952 (pp. 75–82). Paris-Lovain: Gauthier-Villars. Heyting, A. (1958a). Blick von der intuitionistischen Warte. Dialectica, 12, 332–345. Heyting, A. (1958b). Intuitionism in mathematics. In R. ), Philosophy in the midcentury. A survey (pp. 101–115). Firenze: La Nuova Editrice. Heyting, A. (1959). Some remarks on intuitionism. In A. ), Constructivity in mathematics (pp. 72–80). Amsterdam: North-Holland.

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