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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Authors: M. B. Pour-El and J. I. Richards
Title: Computability in analysis and physics
Additional book information: Perspect. Math. Logic, Springer-Verlag, New York, Berlin, Heidelberg, 206 pp. ISBN 0-387-50035-9.

References [Enhancements On Off] (What's this?)

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  • Errett Bishop and Douglas Bridges, Constructive analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 279, Springer-Verlag, Berlin, 1985. MR 804042
  • Douglas Bridges and Fred Richman, Varieties of constructive mathematics, London Mathematical Society Lecture Note Series, vol. 97, Cambridge University Press, Cambridge, 1987. MR 890955
  • Douglas S. Bridges, A constructive look at positive linear functionals on \cal𝐿(𝐻), Pacific J. Math. 95 (1981), no. 1, 11–25. MR 631655
  • [Kr] G. Kreisel, A notion of mechanistic theory, Synthese 29 (1974), 11-26.
  • B. A. Kushner, Lectures on constructive mathematical analysis, Translations of Mathematical Monographs, vol. 60, American Mathematical Society, Providence, RI, 1984. Translated from the Russian by E. Mendelson; Translation edited by Lev J. Leifman. MR 773852
  • J. Myhill, A recursive function, defined on a compact interval and having a continuous derivative that is not recursive, Michigan Math. J. 18 (1971), 97–98. MR 0280373
  • I. G. Petrovskii, Partial differential equations, Translated from the Russian by Scripta Technica, Ltd, Iliffe Books Ltd., London (distributed by W. B. Saunders Co., Philadelphia, Pa.), 1967. MR 0211021
  • Marian Boykan Pour-El and Ian Richards, The wave equation with computable initial data such that its unique solution is not computable, Adv. in Math. 39 (1981), no. 3, 215–239. MR 614161, https://doi.org/10.1016/0001-8708(81)90001-3
  • Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
  • Ernst Specker, Nicht konstruktiv beweisbare Sätze der Analysis, J. Symbolic Logic 14 (1949), 145–158 (German). MR 0031447, https://doi.org/10.2307/2267043
  • [Tu] A. M. Turing, On computable numbers, with an application to the "Entscheidungsproblem", Proc. London Math. Soc. (Ser. 2) 42 (1936), 230-265; corr. ibid. 43(1937), 544-546.

Review Information:

Reviewer: Douglas S. Bridges
Journal: Bull. Amer. Math. Soc. 24 (1991), 216-228
DOI: https://doi.org/10.1090/S0273-0979-1991-15994-X